Frequency Standards and Metrology, Proceedings of the 6th Symposium on Frequency Standards and Metrology : University of St Andrews, Fife, Scotland, 9-14 September 2001 9812777717, 9789812777713

Table of contents :
CONTENTS
Preface
Oral Sessions
Part I Opening Session
Welcome and opening remarks
A Tribute to Helmut Hellwig
Fifty years of atomic frequency standards
Relativistic quantum theory of microwave and optical atomic clocks
Part II OPOs and IR Standards
Self phase-locked sub-harmonic optical parametric oscillators
Continuous-wave optical parametric oscillators as new tools for high resolution spectroscopy
Laser frequency standards with telescopic cavities
Part III Cs Fountains and Comparisons
Cs and Rb fountains: recent results
The atomic caesium fountain CSF1 of PTB
Systematic frequency shifts and quantum projection noise in NIST- Fl
Characterization of the USNO cesium fountain
Comparing high performance frequency standards
Part IV Trapped Ions I
A mercury-ion optical clock
High resolution spectroscopy of a single In+ ion
A frequency standard using the ²S1/2-²F7/2 octupole transition in 171Yb+
Part V Optical Combs I
Optical frequency synthesis with ultrashort pulses
Phase-coherent measurement of optical frequency ratios with femtosecond lasers
Femtosecond optical frequency comb measurements of lasers stabilised to transitions in 88Sr+, 171Yb+, and I2 at NPL
Part VI CPT Standards
Coherent population trapping and intensity optical pumping: on their use in atomic frequency standards
Compact microwave frequency reference based on coherent population trapping
The coherent population trapping maser
All-optical atomic clock based on dark states of 85Rb
Part VII Precision Measurements
A preliminary measurement of h/MCs with atom interferometry
Cold collision frequency shifts and laser-cooled 87Rb clocks
Metrology of hydrogen atom: determination of the Rydberg constant and Lamb shifts
Preliminary results of an accurate measurement of the 4He 2³P0 - 2³P1 fine structure interval
Part VIII Space Clocks
Cold atom clocks in space : PHARAO and ACES
PARCS: a laser-cooled atomic clock in space
New Michelson Morley experiment based on high-Q spherical resonators
Part IX Cold Atom Techniques
Continuous fountain Cs standard: stability and accuracy issues
Mirrors, waveguides and integrated circuits for cold atoms
Atomic multiple beam interferometers and atomic polarised beam interferometers among two excited states
Part X Microwave Standards
A microwave frequency standard based on laser-cooled 171Yb+ ions
Recent developments in cryogenic compensated sapphire oscillators
Current status of cryogenic (50K - 80K) secondary frequency standards for flywheels of atomic fountain clocks
Part XI Cold Atom Optical Standards
Spectroscopy of strontium atoms in the Lamb-Dicke confinement
A 40Ca optical frequency standard at 657 nm: frequency measurements and future prospects
Calcium optical frequency standard
Ultracold metastable calcium atoms
Part XII Trapped Ions II
Quantum computers and atomic clocks
Spectroscopy and precision frequency measurement of the 435.5 nm clock transition of 171Yb+
Ground state cooling and state manipulation of single ions: applications in precision spectroscopy
Part XIII Stable Lasers and Applications
From stable lasers to optical frequency clocks
Testing the foundations of relativity using cryogenic optical resonators
Narrow-linewidth laser system for precise spectroscopy of the indium clock transition
Part XIV Optical Combs II
A femtosecond-laser-based optical clockwork
Optical frequency measurement using an ultra-fast mode-locked laser at NMIJ/AIST
Part XV IR Standards II
Precision measurements and development of infrared absorber stabilised laser systems linked to the 88Sr+ single ion optical frequency standard
Optical frequency standard at 1.5 µm based on Doppler-free acetylene absorption
Absolute frequency measurements with a set of transportable He-Ne/CH4 optical frequency standards and prospects for future design and applications
Poster Sessions
Part XVI Caesium and Rubidium Standards
Proposed laser-cooled 87Rubidium local oscillator
The multiple velocity fountain: a new scheme for the cold collision frequency shift reduction
Preliminary results from a miniature laser-cooled cesium fountain frequency standard
Atoms cooled in a microwave cavity for miniaturized clock
Current status of the miniature optically pumped cesium beam frequency standards at LHA
Characteristics of the Cs atomic fountain frequency standard at NMIJ/AIST
The Cs fountain frequency standard at the Politecnico di Torino: preliminary results
Progress report of 133Cs-Brazilian atomic clock
Part XVII Trapped Ion Optical Standards
Progress towards an improved 88Sr+ single ion optical frequency standard
Single Ca+ ions in a Paul-Straubel trap
Stability and reproducibility of an optical frequency standard based upon the ²S1/2 - ²D5/2 transition in 88Sr+
Resolved sideband cooling of a single trapped strontium ion
Isotope shifts on alkali-like systems calculated by simplified MCHF method
Part XVIII Infrared Standards III
The photon recoil effect in the linear optical Ramsey resonance
Absolute frequency measurements of a methane-stabilized transportable He-Ne laser at 3.39 µm
Doppler-free spectroscopy of CH4 using a CW optical parametric oscillator
The line shape of optical Ramsey resonances
Part XIX Iodine-stabilized Laser Standards
Frequency comparison of I2 stabilised lasers at 532 nm and absolute frequency measurement of I2 absorption lines
A new accurate fit of the hyperfine structure of molecular iodine
Part XX Precision Measurements II
Atomic interferometer and coherent mixing of 2S and 2P states in the hydrogen atom: application to the Lamb shift measurements
Phase noise in atomic interferometer
Acceleration of rubidium cold atoms: Determination of α
Simple pendulum experiment for the determination of the gravitational constant G: Progress report
Part XXI Cold Atom Optical Standards and Techniques
Observation of the 1S0-1D2 forbidden transition in Ca
Optical frequency standards based on cold calcium atoms
Towards a silver atom optical clock
All-solid-state deep-UV coherent light source for laser cooling of silicon atoms
Part XXII Optical Frequency Combs and Stable Lasers
Advances in optical frequency measurement over 30 years
Coupled optoelectronic oscillators: application to low-jitter pulse generation
Absolute optical frequency measurement using a femtosecond laser
Stable double-mode generation in the diode-pumped Nd³+:YAG laser intracavity doubling frequency
Stability of Nd:YAG "flywheel" lasers locked to ultra-high-finesse etalons made from either ULE or or mono-crystalline sapphire
Part XXIII Microwave Standards and Synthesis
Microwave synthesisers for atomic frequency standards
A new high performance microwave synthesis for a compact cesium clock
Advanced PM and AM noise measurements
The impact of prime number theory on frequency metrology
The 'atomic candle': stabilising field amplitude using Rabi-resonances
Recoil effects in microwave atomic frequency standards: an update
Evaluation of the blackbody radiation effects in atomic frequency standards
Sub-doppler polarisation spectroscopy on F4-F'5 transition in Cs
Nonlinear magneto-optical effects in cesium vapour
Part XXIV Space Clocks II
Mercury trapped ion frequency standard for space applications
Testing relativity with clocks on space station
Precise frequency transfer using a WAAS satellite with high-gain antennas
Part XXV 1.5 µm Standards
Absolute frequency stabilisation of 1.54 µm solid-state Er-Yb:glass lasers against 39K and 13C2H2 saturated absorptions
Frequency stabilisation of a semiconductor laser using the Faraday effect of the Rb absorption line: magnetic modulation strength and stability
Frequency stabilisation of a semiconductor laser using both etalon and atomic spectra as frequency references
Increase of the inner second harmonic light of 1.5 µm semiconductor lasers: effect of two optical feedback loops
Broadband frequency noise measurement of semiconductor lasers in the 1550-nm band
Development of a 778 nm rubidium two-photon diode laser frequency standard
List of Participants
Index of Contributors

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Proceedings of the

editor

Patrick G

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Proceedings of the J/"^^ th Symposium

Frequency Standards and Metrology

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th Proceedings of the Js^^

Symposium

Frequency Standards and Metrology

University of St Andrews, Fife, Scotland

9 - 1 4 September 2001

editor

Patrick Gill National Physical Laboratory, Middlesex, Ul

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New Jersey • London • Singapore • Hong Kong Sir

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USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

FREQUENCY STANDARDS AND METROLOGY Proceedings of the Sixth Symposium Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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GOVERNING BOARD Helmut Hellwig (died July 2000) Jacques Vanier Claude Audoin

Andrea de Marchi James C Bergquist

SYMPOSIUM CHAIRMAN Patrick Gill - National Physical Laboratory, UK INTERNATIONAL STEERING COMMITTEE Sergei Bagayev (Russia) Andre Clairon (France) Peter Fisk (Australia) John Hall (USA) Massimo Inguscio (Italy) Shin-ichi Ohshima (Japan) Christophe Salomon (France) Pierre Thomann (Switzerland) Stefan Weyers (Germany)

James Bergquist (USA) Andrea de Marchi (Italy) Patrick Gill (UK) Juergen Helmcke (Germany) Alan Madej (Canada) Brian Petley (UK) Michel Tetu (Canada) Yiqiu Wang (China)

LOCAL COMMITTEE Geoff Barwood Dale Henderson John Laverty Helen Margolis

Malcolm Dunn Hugh Klein Stephen Lea

SPONSORING/ SUPPORTING ORGANISATIONS National Physical Laboratory UK Department of Trade and Industry National Institute of Standards and Technology SYMPOSIUM SECRETARY Bob Angus, NPL, UK SYMPOSIUM CO-ORDINATORS Min Horton, NPL, UK

Tracey Collier, NPL, UK

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Preface It seems clear that the Charter upon which the Frequency Standards and Metrology Symposia are based, is one which has enabled a real sense of discussion and collaboration within our research community. The Symposia now span 30 years, and I have been privileged to attend the last four, from Aussois through to St. Andrews. I have to say that the Symposia prior to St. Andrews have quite simply been the best and most intensive, yet relaxed, and fruitful gatherings of the frequency metrology community that I have attended. The week-long single-session approach, with colleagues spending mealtimes and evenings together seems to work very well. It was against this backdrop that I set out to organise the Sixth Symposium, well aware that previous symposia represented the benchmarks for St. Andrews. I hope that I have succeeded, and the kind feedback from colleagues who enjoyed the science, location and entertainment lead me to believe that this was indeed the case. As to the science, research capability in frequency standards and metrology has, without a doubt, achieved new and significant progress since Woods Hole. Caesium fountain standards are now being evaluated at the part in 10 5, with rubidium fountains also pointing the way to improvements on the cold collisional shift front. In addition, new miniature standards, both CPT - and mini-clocks, have made significant progress. Space clocks for the international space station are getting close to "mission" operation, and stable microwave and optical local oscillators are key constituents in a range of new experiments aimed at improved measurement of fundamental constants, and tests of relativity and fundamental physics. We also heard about new cold atom and ion techniques in related disciplines, which have the potential to influence future frequency metrology. On the optical front, atom and ion frequency standards have gathered serious momentum, with trapped ion linewidths reaching a few hertz. In parallel, femtosecond optical comb metrology has burst onto the scene, with dramatic results. Comb measurement capabilities at the part in 1017 beckon, and we await improvements in the optical standards to make full use of this. The combination of optical frequency standards and the femtosecond comb clockwork has just given us the first demonstration of the optical clock. Undoubtedly, advances in this area will be significant in the period before the seventh Symposium. So, I hope you all find this Proceedings a useful reference for the state-of-the-art in 2001, and thanks to all of you for your contributions. Thanks also to the governing board (Jacques, Helmut, Claude, Andrea and Jim) for their help, support and encouragement for the last two years. Thanks also to my local organising committee, and symposium co-ordinators, Min and Tracey. I look forward to seeing you all again at the seventh Symposium in some years time. NPL, Teddington, January 2002

Patrick Gill

VII

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XI

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CONTENTS Preface

v

Oral Sessions

Part I

Opening Session

Welcome and opening remarks P. Gill

3

A Tribute to Helmut Hellwig R. M. Garvey

4

Fifty years of atomic frequency standards

N.F.Ramsey

8

Relativistic quantum theory of microwave and optical atomic clocks C.J. Borde

Part II

18

O P O s and I R Standards

Self phase-locked subharmonic optical parametric oscillators J.-J. Zondy, V. Laclau, A. Bancel, A. Douillet, A. Tallet, E. Ressayre, M. Le Berre

29

Continuous wave optical parametric oscillators as new tools for high resolution spectroscopy A. Peters, U. StroBner, E. V. Kovalchuk, D. Dekorsy, A. I. Lvovsky, A. Hecker, C. Braxmaier, J. Mlynek, S. Schiller

37

XIV

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Laser frequency standards with telescopic cavities S. N. Bagayev, A. K. Dmitriyev, D. V. Ityaksov, A. A. Lugovoy, V. M. Semibalamut

Part III

45

Cs Fountains and Comparisons

Cs and Rb fountains: recent results S. Bize, Y. Sortais, M. Abgrall, S. Zhang, D. Calonico, C. Mandache, P. Lemonde, P. Laurent, G. Santarelli, C. Salomon, A. Clairon, A. Luiten, M. Tobar

53

The atomic caesium fountain CSF1 ofPTB S. Weyers, A. Bauch, R. Schroder, C. Tamm

64

Systematic frequency shifts and quantum projection noise in NIST- Fl S. R. Jefferts, T. P. Heavner, J. Shirley, T. E. Parker

72

Characterization of the USNO cesium fountain T. B. Swanson, E. A. Burt, C. R. Ekstrom

80

Comparing high performance frequency standards T. E.Parker

88

Part IV

Trapped Ions I

A mercury-ion optical clock J. C. Bergquist, U. Tanaka, R. E. Drullinger, W. M. Itano, D. J. Wineland, S. A. Diddams, L. Hollberg, E. A. Curtis, C. W. Oates, Th. Udem High resolution spectroscopy of a single In+ ion Th. Becker, M. Eichenseer, A. Yu. Nevsky, E. Peik, Ch. Schwedes, M. N. Skvortsov, J. von Zanthier, H. Walther

99

107

XV

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A frequency standard using the 2Sy2 — 2F7/2 octapole transition in S. A. Webster, P. Taylor, M. Roberts, G. P. Barwood, P. Blythe, P. Gill

Part V

l7,

Yb+ 115

Optical Combs I

Optical frequency synthesis with ultrashort pulses Th. Udem, R. Holzwarth, M. Zimmerman, T. W. Hansen

125

Phase-coherent measurement of optical frequency ratios with femtosecond lasers H. R. Telle, N. Haverkamp, J. Stenger

134

Femtosecond optical frequency comb measurements of lasers stabilised to transitions in 88Sr+, 171Yb+, andl2 atNPL S. N. Lea, H. S. Margolis, G. Huang, W. R. C. Rowley, D. Henderson, G. P. Barwood, H. A. Klein, S. A. Webster, P. Blythe, P. Gill, R. S. Windeler

144

Part VI

CPT Standards

Coherent population trapping and intensity optical pumping: on their use in atomic frequency standards J. Vanier, M. Levine, D. Janssen, M. Delaney

155

Compact microwave frequency reference based on coherent population trapping J. E. Kitching, H. G. Robinson, L. W. Hollberg, S. Knappe, R. Wynands

167

The coherent population trapping maser A. Godone, F. Levi, S. Micalizio, J. Vanier

175

All-optical atomic clock based on dark states of Rb T. Lindvall, M. Merimaa, I. Tittonen, E. Ikonen

183

XVI

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Part VII

Precision Measurements

A preliminary measurement ofh/MCs with atom interferometry A. Wicht, J. M. Hensley, E. Sarajlic, S. Chu

193

Cold collision frequency shifts and laser-cooled 87Rb clocks C. Fertig, R. Legere, J. Irfon Rees, K. Gibble, S. Kokkelmans, B. J. Verhaar, J. Prestage, W. Klipstein, D. Seidel, R. Thompson

213

Metrology of hydrogen atom: determination of the Rydberg constant and Lamb shifts G. Hagel, C. Schwob, L. Jozefowski, B. de Beauvoir, L. Hilico, F. Nez, L. Julien, F. Biraben, O. Acef, J.-J. Zondy, A. Clairon

222

Preliminary results of an accurate measurement of the 4He 23P„ - 23Pi fine structure interval G. Giusfredi, P. Cancio Pastor, P. De Natale, L. Fallani, N. Picque, M. Inguscio

230

Part VIII

Space Clocks

Cold atom clocks in space : PHARAO and ACES P. Laurent, M. Abgrall, A. Clairon, P. Lemonde, G. Santarelli, P. Uhrich, N. Dimarcq, L. G. Bernier, G. Busca, A. Jornod, P. Thomann, E. Samain, P. Wolf, F. Gonzalez, Ph. Guillemot, S. Leon, F. Nouel, Ch. Sirmain, S. Feltham, C. Salomon

241

PARCS: a laser-cooled atomic clock in space T. P. Heavner, L. W. Hollberg, S. R. Jefferts, H. G. Robinson, D. B. Sullivan, F. L. Walls, N. Ashby, W. M. Klipstein, L. Maleki, D. J. Seidel, R. J. Thompson, S. Wu, L. Young, E. M. Mattison, R. F. C. Vessot, A. DeMarchi

253

New Michelson Morley experiment based on high-Q spherical resonators M. E. Tobar, J. G. Hartnett, J. Anstie

261

XVII

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Part IX

Cold Atom Techniques

Continuous fountain Cs standard: stability and accuracy issues A. Joyet, G. Mileti, P.Thomann, G. Dudle

273

Mirrors, waveguides, and integrated circuits for cold atoms E. A. Hinds, B. V. Hall, M. P. A. Jones, D. C. Lau, J. Retter, B. E. Sauer, C. J. Vale, K. Furasawa, P. G. Kazansky, D. J. Richardson

281

Atomic multiple beam interferometers and atomic polarised beam interferometers among two excited states A. Morinaga, S. Yanagimachi, T. Aoki

288

Part X

Microwave Standards

A microwave frequency standard based on laser-cooled l7IYb+ ions R. B. Warrington, P. T. H. Fisk, M. J. Wouters, M. A. Lawn

297

Recent developments in cryogenic compensated sapphire oscillators G. J. Dick and R. T. Wang

305

Current status of cryogenic (50 K- 80 K) secondary frequency standards for flywheels of atomic fountain clocks J. G. Hartnett, M. E. Tobar, E. N. Ivanov, C. R. Locke

313

Part XI

Cold Atom Optical Standards

Spectroscopy of strontium atoms in the Lamb-Dicke confinement HLKatori

323

A 40Ca optical frequency standard at 657 nm: frequency measurements andfuture prospects E. A. Curtis, C. W. Oates, S. A. Diddams, Th. Udem, L. Hollberg

331

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XVIII

Calcium opticalfrequency standard F. Riehle, G. Wilpers, U. Sterr, T. Binnewies, J. Helmcke

339

Ultracold metastable calcium atoms J. Griinert, A. Hemmerich

347

Part XII

Trapped Ions II

Quantum computers and atomic clocks D. J. Wineland, J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano

361

Spectroscopy and precision frequency measurement of the 435.5 nm clock transition of171Yb+ Chr. Tamm, T. Schneider, E. Peik

369

Ground state cooling and state manipulation of single ions: applications in precision spectroscopy C. F. Roos, D. Leibfried, F. Schmidt-Kaler, J. Eschner, R. Blatt

376

Part XIII

Stable Lasers and Applications

From stable lasers to optical frequency clocks J. L. Hall, J. Ye, L.-S. Ma, J.-L. Peng, M. Notcutt, J. D. Jost, A.Marian

387

Testing the foundations of relativity using cryogenic optical resonators S. Schiller, C. Braxmaier, H. Miiller, S. Herrmann, J. Mlynek, A.Peters

401

Narrow-linewidth laser system for precise spectroscopy of the indium clock transition A. Yu. Nevsky, M. Eichenseer, J. von Zanthier, H.Walther

409

XIX

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Part XIV

Optical Combs II

A femtosecond-laser-based optical clockwork S. A. Diddams, Th. Udem, K. R. Vogel, L.-S. Ma, L. Robertsson, C. W. Oates, E. A. Curtis, W. M. Itano, R. E. DruUinger, D. J. Wineland, J. C. Bergquist, L. Hollberg

419

Optical frequency measurement using an ultra-fast mode-locked laser at NMIJ/AIST K. Sugiyama, A. Onae, F.-L. Hong, H. Inaba, S. N. Slyusarev, T. Ikegami, J. Ishikawa, K. Minoshima, H. Matsumoto, J. C. Knight, W. J. Wadsworth, P. St. J. Russell

427

Part XV

IR Standards II

Precision measurements and development of infrared absorber stabilised laser systems linked to the S8Sr+ single ion optical frequency standard A. A. Madej, A. Czajkowski, K. J. Siemsen, J. E. Bernard, L. Marmet, P. Dube

437

Optical frequency standard at 1.5 fim based on Doppler-free acetylene absorption A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R.Felder, O. Acef

445

Absolute frequency measurements with a set of transportable He-Ne/CH4 optical frequency standards and prospects for future design and applications M. Gubin, E. Kovalchuk, E. Petrukhin, A. Shelkovnikov, D. Tyurikov, R. Gamidov, C. Erdogan, E. Sahin, R. Felder, P. Gill, S. N. Lea, G. Kramer, B. Lipphardt

453

XX

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Poster Sessions

Part XVI

Caesium and Rubidium Standards

Proposed laser-cooled Rb local oscillator S. R. Jefferts, D Kujundzic, T. P. Heavner, T. E. Parker

463

The multiple velocity fountain: a new scheme for the cold collision frequency shift reduction F. Levi, A. Godone, L. Lorini, S. R. Jefferts, T. P. Heavner, C. Calosso

466

Preliminary results from a miniature laser-cooled cesium fountain frequency standard T. P. Heavner, S. R. Jefferts, T. E. Parker

469

Atoms cooled in a microwave cavity for a miniaturized clock P-E. Pottie, Th. Zanon, P. Petit, N. Dimarcq, S. Bila, M. Aubourg

472

Current status of the miniature optically pumped cesium beam frequency standards at LHA V. Hermann, L. Chassagne, T. Zanon, C. Audoin, P. Cerez, G. Theobald

475

Characteristics of the Cs atomic fountain frequency standard atNMIJ/AIST T. Kurosu, Y. Fukuyama, Y. Koga, S. Ohshima

478

The Cs fountain frequency standard at the Politecnico di Torino: preliminary results G. A. Costanzo, C. E. Calosso, A. De Marchi

480

Progress report of'33Cs Brazilian atomic clock M. S. Santos, F. Teles, D. V. MagaMes, A. Bebeachibuli, V. S. Bagnato

483

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Part XVII

Trapped Ion Optical Standards

Progress towards an improved Sr+ single ion optical frequency standard P. Dube, L. Marmet, J. E. Bernard, K. J. Siemsen, A. A. Madej

489

Single Ca+ ions in a Paul-Straubel trap M. Knoop, C. Champenois, P. Courteille, M. Herbane, M. Houssin, M. Vedel, F. Vedel

492

Stability and reproducibility of an optical frequency standard based upon the 2S i/2 - 2D s/2 transition in sSr+ G. P. Barwood, P. Gill, G. Huang, H. A. Klein

495

Resolved sideband cooling of a single trapped strontium ion A. G. Sinclair, M. A. Wilson, V. Letchumanan, P. Gill

498

Isotope shifts on alkali-like systems calculated by a simplified MCHF method K. Gao, Y. Li, L. Wu, X. Zhu

501

Part XVIII

Infrared Standards III

The photon recoil effect in the linear optical Ramsey resonance G. Kramer

507

Absolute frequency measurements of a methane-stabilised transportable He-Ne laser at 3.39 pm P. V. Pokasov, R. Holzwarth, Th. Udem, M. Zimmermann, J. Reichert, M. Niering, T. W. Hansen, A. K. Dmitriyev, S. N. Bagayev, P. Lemonde, G. Santarelli, P. Laurent, M. Abgrall, A. Clairon, C. Salomon

510

Doppler-free spectroscopy ofCH4 using a cw optical parametric oscillator E. V. Kovalchuk, D. Dekorsy, A. I. Lvovsky, C. Braxmaier, J. Mlynek, S. Schiller, A. Peters

513

The line shape of optical Ramsey resonances D. D. Krylova

516

xxii

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Part XIX

Iodine-stabilized Laser Standards

Frequency comparison ofh stabilised lasers at 532 nm and absolute frequency measurement ofI2 absorption lines A. Yu. Nevsky, R. Holzwarth, M. Zimmermann, Th. Udem, T. W. Haensch, J. von Zanthier, H. Walther, P. V. Pokasov, M. N. Skvortsov, S. N. Bagayev, H. Schnatz, F. Riehle

521

A new accurate fit of the hyperfine structure of molecular iodine Ch. J. Borde, F. Du Burck, A. N. Goncharov

524

Part XX

Precision Measurements II

Atomic interferometer and coherent mixing of2S and 2P states in the hydrogen atom: application to the Lamb shift measurements V. G. Pal'chikov, Yu. L. Sokolov, V. P. Yakovlev Phase noise in atomic interferometer A. Landragin, J. Fils, F. Yver, D. Hollevile, N. Dimarcq, A. Clairon Acceleration of rubidium cold atoms: determination of a R. Battesti, C. Schwob, B. Gremaud, S. Guellati, F. Nez, L. Julien, F. Biraben Simple pendulum experimentfor the determination of the gravitational constant G: progress report A. De Marchi, M. Ortolano, M. Berutto, F. Periale

529

532

535

538

Part XXI Cold Atom Optical Standards and Techniques

Observation of the So— D2 forbidden transition in Ca N. Beverini, E. Maccioni, A. Ruffini, F. Sorrentino, V. Baraulia

543

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XXIII

Opticalfrequency standards based on cold calcium atoms R. L. Cavasso-Filho, D. A. Manoel, D. R. Ortega, A. Scalabrin, D. Pereira, F. C. Cruz

546

Towards a silver atom optical clock T. Badr, S. Gu6randel, Y. Louyer, S. Challemel du Rozier, M. D. Plimmer, P. Juncar, M. E. Himbert

549

All-solid-state deep-UV coherent light source for laser cooling of silicon atoms H. Kumagai, K. Midorikawa, Y. Asakawa, M. Obara 552

Part XXII

Optical Frequency Combs and Stable Lasers

Advances in optical frequency measurement over 30 years D. J. E. Knight

557

Coupled optoelectronic oscillators: applications to low-jitter pulse generation N. Yu, M. Tu, L. Maleki 560 Absolute optical frequency measurement using a femtosecond laser G. D. Rovera, J.-J. Zondy, O. Acef, F. Ducos, J.-P. Wallerand, P. G. Antonini, J. C. Knight, P. St. J. Russel

564

Stable double-mode generation in the diode-pumped Net*:YAG laser intracavity doubling frequency R. A. Karle, V. N. Petrovskiy, E. D. Protsenko, V. M. Yermacenko, D. V. Zelenin, R. R. Karle

567

Stability ofNd.YAG "flywheel" lasers locked to ultra-high-finesse etalons made from either ULE or or mono-crystalline sapphire M. Oxborrow, S.A. Webster, P. Gill

571

Part XXIII

Microwave Standards and Synthesis

Microwave synthesisers for atomic frequency standards A. Sen Gupta, J. F. Garcia Nava, C. Nelson, D. A Howe, F. L. Walls

577

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xxiv

A new high performance microwave synthesis for a compact cesium clock R. Barillet

580

Advanced PM and AM noise measurements E. Rubiola, V. Giordano

583

The impact of prime number theory on frequency metrology M. Planat

586

The 'atomic candle': stabilising field amplitude using Rabi-resonances J. Camparo

590

Recoil effects in microwave atomic frequency standards: an update P. Wolf, S. Bize, A. Clairon, A. Landragin, P. Laurent, P. Lemonde, Ch. J. Borde

593

Evaluation of the blackbody radiation effects in atomic frequency standards V. G. Pal'chikov, Yu. S. Domnin and A. V. Novoselov

597

Sub-doppler polarisation spectroscopy on F4—F'5 transition in Cs Yu. S. Domnin, V. M. Tatarenkov, A. V. Novoselov, V. G. Pal'chikov

600

Nonlinear magneto-optical effects in cesium vapour V. Barychev, V. Pal'chikov, A. De Marchi

603

Part XXIV

Space Clocks II

Mercury trapped ion frequency standardfor space applications R. L. Tjoelker, E. Burt, S. Chung, R. Glaser, R. Hamell, L. Maleki, J. D. Prestage, N. Raouf, T. Radey, G. Sprague, B. Tucker, B.Young

609

Testing relativity with clocks on space station J. A. Lipa, J. A. Nissen, S. Wang, D. A. Strieker and D. Avaloff

615

Precise frequency transfer using a WAAS satellite with high-gain antennas M. Weiss, M. Jensen, P. Fenton, E. Powers, B. Klepczynski

619

XXV

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Part XXV

1.5 pm Standards

Absolute frequency stabilisation of 1.54 fjm solid-state Er-Yb:glass lasers against 39K and ,3C2H2 saturated absorptions C. Svelto, G. Galzerano, E. Bava, F. Ferrario, A. Arie, R. Klein, M. A. Arbore, M. M. Fejer, A. Onae, M. Marano

625

Frequency stabilisation of a semiconductor laser using the Faraday effect of the Rb absorption line: magnetic modulation strength and stability T. Saga, T. Nimonji, S. Ito, T. Sato, M. Ohkawa, T. Maruyama, M. Shimba

629

Frequency stabilisation of a semiconductor laser using both etalon and atomic spectra as frequency references T. Aiba, Y. Ohsawa, T. Sasaki, T. Sato, M. Ohkawa, T. Maruyama, M. Shimba

632

Increase of the inner second harmonic light of 1.5 fim semiconductor lasers: effect of two optical feedback loops M. Sakai, T. Ichiba, T. Seki, Y. Ohsawa, T. Sato, M. Ohkawa, T. Maruyama, M. Shimba

635

Broadband frequency noise measurement of semiconductor lasers in the 1550-nm band P. Tremblay, C. S. Turcotte, M. Bondiou, J. Genest, M. Allard, P. Levesque, J.-P. Bouchard, C. Latrasse, M. Poulin, M. Tetu

638

Development of a 778 nm rubidium two-photon diode laser frequency standard C. S. Edwards, G. P. Barwood, P. Gill, W. R. C. Rowley 643

List of Participants

647

Index of Contributors

651

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Parti

Opening Session

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WELCOME & OPENING REMARKS

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PATRICK GILL

I would like to begin the week here in St. Andrews by welcoming you all to this Symposium on Frequency Standards and Metrology. The Symposium is the sixth in a series of Symposia stretching back over 30 years. The first was organised by Jacques Vanier in 1971 at Foret Montmorency in Quebec. It was followed by Copper Mountain (1976), Aussois (1981), Ancona (1988) and Woods Hole (1995). Copper Mountain was the responsibility of Helmut Hellwig, who sadly died last year. Over the last 30 years, Helmut has been a driving force for the shape and scope of the Symposia, and Michael Garvey will shortly offer a tribute to him. The following symposia were organised by Claude Audoin, (Aussois), Andrea de Marchi (Ancona) and Jim Bergquist (Woods Hole). The significant lapse of time between each Symposium has been intentional, in order to enable new, significant and fundamental ideas to surface in the time between, and to allow previously emergent ideas to mature to a level where their real contribution to frequency standards can be evaluated. Within the symposium framework, such new ideas can be discussed and reviewed by the representatives from the complete international frequency standards community. For example, a single event from Woods Hole was the appearance of the first atomic fountain standards in response to previous laser cooling advances in the 80s. As we go into the Sixth Symposium, perhaps it is the advent of optical combs over the past two years, where major advances have been made. This has led very recently to the first optical clock demonstration. I have to say that, even at Woods Hole in 1995, none of us surmised that the optical clock threshold upon which we now stand, would be a reality rather than a future dream. So without further ado, I will hand over to Jim Bergquist to introduce Mike Garvey's tribute to Helmut, and following that, ask Norman Ramsey to set the Sixth Symposium in context, with a review of frequency standards spanning from fifty years ago up to the present day.

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A TRIBUTE TO HELMUT HELLWIG

R. MICHAEL GARVEY Datum Timing, Test and Measurement 34 Tozer Road, Beverly MA 01915 USA

I'd like to thank the Symposium organizers for the opportunity to speak for a few minutes about Helmut Hellwig. As most of you know Helmut died last July. Today I want to look retrospectively at Helmut's career and at the many contributions that made him so important to many of us in the time and frequency community. Helmut was born in Berlin Germany in 1938. He completed a Master of Science degree in 1963 and a Doctorate in electrical engineering in 1966, both from the Technical University of Berlin. During that period Helmut was a researcher at the Heinrich Hertz Institute in Berlin. He immigrated to the United States in 1966 and became a U.S. citizen in 1972.

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Helmut's first worked as a Research Physicist for the US Army Electronics Command in Ft. Monmouth, NJ. Helmut left Ft. Monmouth in 1969 to work at the National Bureau of Standards in Boulder, Colorado. Many of us know Helmut from the 10 years he worked at NBS. Working in the Time and Frequency Division, Helmut progressed from the position of Physicist to Section Chief and then to Associate Division Chief. This was the time of the genesis of this Symposium. Helmut was, as Andrea DeMarchi reminded us at Woods Hole six years ago, one of the three founding fathers of the Symposium on Frequency Standards and Metrology: Jacques Vanier organized the first Symposium in 1971 at Foret Montmorency (Quebec), Helmut organized the second at Copper Mountain, (Colorado) in 1976, and Claude Audoin organized the third at Aussois (Haute Savoie) in 1981. In 1979, Helmut left NBS to take the Presidency of Frequency and Time Systems in Danvers, Massachusetts. For 7 years Helmut led FTS along a path of growth: first with government financing for its new manufacturing facility and then by obtaining a new U.S. parent which enabled FTS to enter the GPS cesium clock program. In 1986 Helmut returned to NBS as Associate Director. Then, in 1990 he was appointed director of the Air Force Office of Scientific Research where he was responsible for management of the entire basic research program of the US Air Force. In 1996 Helmut was appointed Deputy Assistant Secretary for Science, Technology and Engineering, Office of the Secretary of the Air Force. In that position, he was responsible for all Air Force investments in science and technology. Helmut retired in 1999. These are impressive credentials for any professional individual; there is, however, a much deeper and more personal side of Helmut which many of us experienced. Helmut always possessed the fortitude and stubbornness to look to the future with an eye for constructive change and improvement. The status quo was never good enough for him. Helmut made the kind of waves that led to growth for all those around him. He sought to surround himself with capable, bright and innovative people. The team that he began to assemble in the mid 1970s at NBS included Fred Walls, Sam Stein, and David Wineland to name a few. Research had essentially been abandoned in the Time and Frequency Division until Helmut arrived. He tirelessly pursued internal and external support to launch the fledgling research effort. When he recruited Dave Wineland in 1975, he clearly believed that not only was laser cooling of atoms and ions possible, but that it would revolutionize the world of atomic frequency standards and maybe all of atomic, molecular and optical physics. I think that we would all agree, today, looking back, that Helmut's beliefs

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were correct. The team he developed at NIST continues today with the success, at long last, of developing the single Hg-ion clock. Others will report, in this Symposium, of similar research toward the development of optical clocks based on atoms and ions. I got to know Helmut as my career began in time and frequency. Having finished my thesis work in molecular spectroscopy, I looked for a job. Helmut helped me find a post doctoral position at NBS in the fall of 1976. Even before I started work in Boulder, he found support for me to attend the Second Symposium on Frequency Standards and Metrology at Copper Mountain. When Helmut left NBS in 1979 I took the opportunity to join him at FTS. We were a small company with an enthusiastic and capable leader. With the same determination, endless energy and stamina that he had applied to the NBS team, Helmut grew a fledgling company to a strong industry player. Those who have worked with Helmut know that he was always brutally direct and honest; this trait sometimes worked in his disfavor for those who didn't want to hear the unvarnished truth. Although he was strong willed and certain, he openly sought and accepted advice from those around him. In group meetings, he would outline his position, present supporting arguments and then actively seek constructive criticism. Usually he was right; he would graciously reverse himself if the contrary position could be better supported. With whomever Helmut worked, he aggressively fought for "his team". And then, when he moved on, he left systems, culture and philosophies in place which made the organizations stronger and better able to "weather the storm". On the personal side, Helmut made little distinction between his professional work and his personal life. He invited colleagues into his home and into his life. Upon the arrival of a new international colleague at NBS, Helmut would go to the airport to personally meet this new colleague. Helmut and Thekla would invite these new friends into their home, making them feel comfortable in their new environment. In a spirit of cooperation and support, Helmut would organize group events; a frequently repeated favorite of many was a pig roast. Parties at the Hellwig residence were always fun: everyone was invited and, of course, the food, wine and beer were exceptional. Helmut loved the outdoors; hunting was one of his favorite weekend activities in Colorado. He would leave Boulder well before daylight to be in position when the sun rose. Professional colleagues were included in this recreation if they enjoyed it. I recall a time when Helmut took Raymond Besson and me camping and duck hunting in western Colorado. We slept in small tents to keep warm; upon waking, we found a light dusting of snow on our sleeping bags.

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As I have gathered material for this presentation, I have talked to a large number of Helmut's past coleagues. Some of their comments are: "Helmut was the first boss I've had who didn't view me as a competitor" He was "... a mentor, head cheerleader, bill payer and one heck of a great boss" So, as we go forward during the next five days, let us remember Helmut as, not only a founder of this conference, but as one, were he here today, who would challenge our ideas, join us in our food and drink and push us to achievements we wouldn't otherwise attempt.

Acknowledgments I would like to thank of Helmut's many friends and colleagues for their contributions to this retrospective. I particular, I want to thank Jim Bergquist for his thoughts.

FIFTY YEARS OF ATOMIC FREQUENCY STANDARDS

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NORMAN F. RAMSEY Lyman Laboratory of Physics, Harvard University Cambridge, Massachusetts 02138, USA This brief review of the history of atomic frequency standards includes: atomic beam magnetic resonance, microwave absorption and optical pumping, atomic masers, lasers, laser cooling and laser cooled atoms and ions at optical frequencies.

1. Introduction The idea for atomic frequency standards and clocks has a long history. James Clerk Maxwell, in his 1873 Treatise [1] wrote "A more universal unit of time might be found by taking the periodic time of vibration of the particular kind of light whose wave length is the unit of length." There was no way to realize this excellent idea in 1873, but beginning in 1937 a series of inventions and developments eventually made atomic frequency standards possible. Time and frequency measured with atomic clocks are now the most accurately measurable of all physical quantities.

2. Atomic Beam Magnetic Resonance (Cs) 1937 -1940: Atomic beam magnetic resonance frequency standards and clocks were the first high precision standards and they are still used for the international definition of the second and for many precision measurements. These clocks grew out of the molecular beam magnetic resonance, method which was invented by 1.21. Rabi [2,3] in 1937. Rabi, in discussing the changes in orientation states of an atom passing by successive static fields of different directions, wrote a great paper [2] entitled "Space quantization in a gyrating magnetic field\ This publication provided the fundamental theory for all later magnetic resonance experiments, but six months elapsed before Rabi [2,4], after a meeting with C.J. Gorter [4,5], invented the molecular beam magnetic resonance method. In this method a beam of molecules is deflected by an inhomogeneous magneticd field and refocused by a second magnetic field. An oscillatory magnetic field is applied in the intermediate region. If the frequency of the oscillator equals a Bohr frequency, v 0 = (Ef - Ei )/h, of the atom, the atom may make a transition to another state with different magnetic properties and the refocusing will fail with a reduction in the beam intensity; therefore the frequency at which there is the biggest change of beam intensity will be that for which v = v0. Rabi, Zacharias, Millman, and Kusch [3] observed the

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9 first magnetic resonance in 1938 but the resonance frequency was proportional to the external magnetic field and therefore not suitable for an atomic clock. The first magnetic resonance observations of internal molecular energies were made by Kellogg, Rabi. Ramsey and Zacharias [4]in 1939 and the first atomic hyperfine transitions changing the value of F (F = I + J) were observed in 1940 by Kusch, Millman and Rabi [4], including the Cs transition that is now used for atomic clocks. 1940 - 1945: The Columbia molecular beam laboratory was closed during World War II. Rabi was asked to give the Richtmyer Lecture to the AAPT and APS and talked about molecular beam resonance, the possibility of atomic clocks and even the possibility of using them to test the gravitational red shift. William Lawrence wrote this up in the NY Times article of January 21, 1945. This article thus became the first publication on atomic clocks in modern times. Although an atomic beam frequency standard could have been made in 1945, it would not have been better than the best pendulum standard because the resonance width becomes broader with diminished length of the resonance region, but phase coherency requires that length to be less than a half wave length. 1949-1950: This last barrier to accurate atomic frequency standards was overcome in 1949 by N. F. Ramsey [6], who invented the methods of separated and successive oscillatory fields. In the separated oscillatory fields method the oscillatory fields are coherently applied to the atom only as it enters or leaves the transition region. The need for coherency requires only that each separated oscillatory field region be shorter than half a wave length, while the sharpness of the resonance is determined by the separation of the oscillatory fields and can be many wave lengths. As a result much narrower resonances are observed and much higher frequencies can be used. In 1950 Kolsky, Phipps, Ramsey and Silsbee [4] successfully used this method in molecular beam spectroscopy. 1952-1954: Sherwin, Lyons, McCracken and Kusch [4] started building an atomic Cs clock at NBS, but in 1952 this effort was unfortunately abandoned in favor of a microwave NH3 clock, which eventually did not achieve high accuracy.. In 1954 Zacharias [4,5] attempted to obtain an even narrower separated oscillatory fields resonance in a "fountain" experiment. Very slow atoms were allowed to travel upward through a first oscillatory field and then to fall under gravity to pass again through the same field a fraction of a second later. The resulting resonance should have been very narrow. Unfortunately the experiment failed due to the very slow atoms being scattered away as they emerged from the thermal source. Many years later, this experiment was successfully revived by S. Chu and others with laser cooled atoms, as discussed in Section 6.

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1955:- .... Zacharias, Holloway, McCoubrey and others at MIT and the National Company in 1955 developed [5] the first commercial atomic clock called the "Atomichron". It used atomic Cs and the separated oscillatory fields resonance method. This clock required many ingenious engineering developments to obtain high reliability and a much longer operating life (years instead of hours). A number of these were purchased by the U.S. Army Signal Corps and by commercial organizations Also in 1955 Essen and Parry at the National Physical Laboratory in England constructed and operated the first atomic clock that contributed to a national time and frequency standard. It was based on Cs and the separated oscillatory field method. Beginning in 1955 Ramsey published a series of theoretical papers analyzing possible errors in atomic clocks and the means by which these errors could be avoided or reduced. 1956-.... : From 1956 onward many Cs atomic clock improvements were developed at universities, national laboratories and industries around the world. These improvements included better excitation, longer beams, reversed beams, reduced size and weight, improved cavities, optical pumping, laser state selection,.... The organizations contributing included NIST (formerly NBS), PTB, NRC, NPL, Bureau de l'Heure, National Co., Bomac, Varian, HP, Frequency & Time Systems ... The contributing scientists and engineers included Mockler, Beehler, Barnes, Hellwig, Wineland, Itano, Drullinger, Kartaschoff, De Marchi and others. [7]. 1967 - . . . : In 1967 the unit of time, the second, was defined in terms of the Cs hyperfine oscillations. Subsequent international agreements provided an international UTC based on atomic time but with leap seconds introduced whenever necessary to keep UTC within 0.7 seconds of GMT (Greenwich mean time} as determined by astronomical observations. In subsequent years up to the present the accuracies of the best Cs beam clocks have steadily improved and in 2001 the unit of time continues to be defined in terms of the Cs frequency. 3. Microwave Absorption and Optical Pumping 1934: In a great pioneering experiment in 1934, Cleeton and Williams [5] observed a single broad microwave absorption resonance in NH3 corresponding to the tunneling transition between states with the N being on one side or the other of the H3 plane. Unfortunately there was no follow up for this first microwave absorption spectroscopy during the next eleven years.

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1946 -1947: After the eleven year gap and the development of microwave radar, there was a veritable explosion of microwave spectroscopy publications in 1946, with papers [5] by Bleaney, Penrose, Beringer, Townes, Dicke, Lamb, Becker, Autler, Strandberg, Dailey, Khyl, VanVleck, Wilson, Dakion , Good, Cole, Hershberger, Lambert, Watson, Roberts, Beers, Hill, Merrit and Walter. There were 79 published papers in 1947 and many more in subsequent years.. 1948: In 1948 Lyons and others [5] at the NBS made a microwave clock based on the NH3 inversion transition, but it was soon abandoned because of its instability. 1949: Kastler and Brossel [5] in 1949 developed the powerful technique of optical pumping, in which the occupancy of certain states could be enhanced by inducing transitions with light. Much stronger magnetic resonance and microwave absorption signals could then be obtained.. Unfortunately the optical pumping radiation also induces a light shift of the resonance frequency, a serious disadvantage for a frequency standard, but means were eventually developed by Cohen-Tannoudji and others, to reduce or control the light shifts. 1953: -... : Dicke, Kastler and others [5], beginning in 1953, introduced the use of inert buffer gases like He to reduce the first order Doppler shifts by reducing the atoms average velocity and to reduce the numbers of wall collisions. They also used cells coated with various waxy substances to diminish the frequency shifts caused by wall collisions. 1956: In 1956 Dehmelt [5] increased the sensitivity of optically pumped cells by the process of "shelving" in which a lower frequency clock transition is detected by changed optical fluorescence depending on whether one of the clock states is occupied. 1958: Bender, Dehmelt, Robinson , Dicke [5] and others in 1958 further increased the sensitivity and accuracy of optically pumped Rb clocks by using hyperfme filtering to reduce the effects of unwanted spectral lines. 1960 -...: Many engineering improvements were made in optically pumped Rb clocks and some optically pumped Rb frequency standards were qualified by NASA for use in space missions. Some of the institutions participating in this work were Efratom, ITT, Varian, GTC, FRK, STL, General Radio. FRK, EG&G and Frequency & Time Syst. Some of the participating scientists and engineers were Arditi, Carver, Andres, Bell, Bloom, Stralemeyer, Jechert and Riley.

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12 Optically pumped Rb cells are now highly stable with an Allan variance, ay(x) of 5 x 10"14 for periods x of 105 seconds and 5 x 10"13 for 1,000 second periods. Optically pumped Rb clocks are used for many purposes because of their high stability, lower cost and reliability. They are, for example, extensively used in the GPS satellites . 4. Atomic Masers (H & Rb) 1954: Gordon Zeiger and Townes [5] made the world's first maser in 1954. It used electric dipole moments and the tunneling transition of NH3. At that time it was thought that a maser could not be made using atomic hyperfine structure because of the much smaller dipole moments and transition energies. 1958: In 1958 Kleppner, Ramsey and Fjelstadt [5] obtained sharp resonances with Cs atoms trapped in an evacuated bottle long enough for the atoms to undergo several hundred wall collisions during the resonance period. They then realized that atomic hydrogen could probably be stored longer, but the sensitivity of hydrogen detection at that time was very poor, so they calculated the possibility of the hydrogen resonance being detected by its effect on the radiation field. Due to the narrowness of the resonance and long storage time they found that the detection should be easy and that the device could even be operated as an atomic maser. 1960: In 1960 Goldenberg, Kleppner and Ramsey [8] constructed and successfully operated the first atomic hydrogen maser. Hydrogen atoms in the higher F = 1 hyperfine state are focussed by the six-pole magnet to continuously load the teflon lined quartz bottle in a tuned cavity with the higher energy atoms. The system spontaneously oscillates as a maser and emits a highly stable signal that can be used as a clock or frequency standard. 1963 -1967: Bender [5,8] in 1963 pointed out that spin exchange collisions apparently could provide a significant reduction to the accuracy of a hydrogen maser clock. But Crampton [5]in a series of papers showed that, if the maser were tuned to make the frequency independent of the line resonance width, the spin exchange shift would be exactly balanced by the cavity pulling effect. 1967 - 2001: Since 1967 many variations and improvements have been made in hydrogen masers by scientists throughout the world and especially in the United States, Russia and Canada. The principal contributing scientists and engineers include Vessot, Kleppner, Ramsey, Crampton, Peters, Vanier, Levine, Cutler, Berg, Reinhardt, Audoin, Grivet, Vanier, Kartaschoff, Brenner and Zitzewitz.

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Although atomic hydrogen has many advantages, other atoms can also be used. Vanier, Novick and others for example have done some work on a rubidium atomic maser. The hydrogen maser has the advantage of being a free running atomic oscillator with high stability, narrow band width, low noise and relatively high output power. Its Allan variance , ay(x), is 5 x 10"16 for periods T of 1,000 seconds. These characteristics make hydrogen masers particularly useful in radio-astronomy with very long baseline interferometers (VLBI). The high power and stability of hydrogen masers have made them particularly useful as fly-wheel oscillators for much lower powered devices, such as laser cooled atomic frequency standards. Many national standards laboratories use the hydrogen maser for broadcasting time signals even though the maser frequency may be steered by other standards. The hydrogen maser has also been used in various tests of the special and general theories of relativity including the gravitational red shift. 5. Lasers 1954: In 1954 Gordon , Zeiger and Townes [5] used a state selected NH3 beam to make the first maser. At that time it was thought the maser principle could not be applied at optical frequencies because the phases would not be coherent due to the wave lengths being smaller than the size of the excitation region. 1958: Four years later, Schalow and Townes wrote a fundamental theoretical paper noting that the optically excited states were so short lived in the laser that the excited molecules moved less than half a wave length during their excited lifetime. As a result coherency and maser actions could be maintained at light frequencies and lasers should be possible. 1960 -... : Maiman in 1960 reported his success in making the first operating laser. The active material in this laser was ruby. The next year Javan, Bennett and Herriot reported their success in making the first gas laser with a helium- neon gas mixture. Subsequently successful lasers have been made of various designs and with may different active materials. The earliest uses of lasers in atomic clocks were as auxiliary components, such as state selectors in microwave frequency standards. 1961 -1970: Due to first order Doppler shifts, the first lasers produced a very broad spectrum at frequencies primarily determined by the laser dimensions. However there was a much narrower intensity dip which Lamb [9] explained as due to both of the oppositely directed running, waves being resonant at the same frequency for molecules that were motionless.

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Double resonance and laser saturated absorption spectroscopy techniques for eliminating first order Doppler effects were developed by Schossberg, Javan, Barger, Hall, Borde, Hansch, Levinger, Schawlow and others [9]. In 1970 Visikenko, Chebotaev and Shishaev [9] introduced the powerful method of two-photon Doppler free absorption spectroscopy. In this method two photons at the same frequency moving in opposite directions have to be absorbed to provide the transition energy, so the Doppler shifts cancel in the sum, independent of the molecular velocity. 1970 - 1888: For the frequencies of lasers to be accurately compared with time and frequency standards at lower frequencies, chains for frequency multiplying, dividing and adding were required. A number of these were developed by Javan, Hall, Borde, Evenson, HSnsch and others, but, for many years, they were quite complicated and laser frequency standards were chiefly used to compare one optical frequency with another. This problem has recently been overcome, as discussed in Section 7. 6. Laser Cooling 1975 : In the early 1970's, it appeared that all atomic frequency standards would reach a fundamental accuracy limit due to the second order Doppler shift or the relativistic effect that a moving clock, such as an atom, runs slow. At typical atom thermal speeds this limitation would be around 10"17. Prospects for overcoming this limit for both trapped ions and trapped atoms arose when in 1975 Wineland and Dehmelt proposed laser cooling for ions and in the same year Hansch and Schalow proposed laser cooling for atoms. Laser cooling is a method by which beams of light can be used to slow the speeds of atoms and ions and thereby reduce their temperatures (11,12). The basic mechanism utilizes laser beams tuned slightly lower in frequency than a strongly allowed optical resonance transition. When the velocity of the ion or atom is directed against the laser beam, the light frequency in the ion's frame is Doppler shifted closer to resonance, and the light absorption takes place at a higher rate than when the velocity is in the same direction as the laser beam. Since the photons are re-emitted in random directions, the net effect over a motional cycle is to damp the ion's velocity by absorption of photon momentum. With pairs of counter propagating laser beams along each of three mutually perpendicular axes, the atom is slowed down in whatever direction it moves to provide a three-dimensional laser-cooled region in which the atoms move very sluggishly. 1980-... : Although Wineland, Dehmelt and others [5] in 1980 showed experimentally that laser cooling worked for trapped ions, it was initially difficult to

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15

make an accurate ion clock because the charged ions repelled each other and gave rise to added motions that reduced accuracy. This difficulty was overcome partially by L. Cutler and others with the use of an elongated sparsely filled ion trap. The difficulty was later fully overcome by the use of a single ion and by partially compensating for the reduced intensity by Dehmelt's process of "shelving" discussed in section 3. Laser traps for ions are much weaker than ion traps, so several years of additional research were required before Chu and his associates [5,10,11] in 1985 obtained the first laser cooled trapped atoms in a viscous fluid of photons, which they called "optical molasses". Even then, the laser cooled trapped atoms were not suitable for frequency standards because the laser trapping fields distorted the desired resonance. Chu, Kasevich and others overcame [17] this problem in 1989 by combining laser cooling with Zacharias's atomic fountain method, discussed n Section 2. Chu laser cooled trapped atoms on a reference frame that was moving upward at about a meter per second. He then turned off the trapping laser while the atoms coasted through the oscillatory field region and then turned under gravity to fall through the oscillatory field again to give a narrow separated oscillatory fields resonance. Originally it was theoretically expected that laser cooling could not cool atoms below the Doppler limit of 200 micro K, but Phillips [14] and his associates in 1988 tested to see if this low temperature could be reached. To their surprise they measured temperatures much below the Doppler limit. This was eventually explained by CohenTannoudji, Chu and others as due to an additional and unexpected cooling mechanism called "Sisyphus cooling". With this understanding, further laser cooling techniques have been developed to reach a temperature of 0.003 micro K, which is lower than any temperature in the universe. Although laser cooling initially was developed for atomic frequency standards, it has also been used to produce Bose-Einstein condensation [BEC]. Cohen-Tannoudji, Aspect, Dalibard, Salomon and others are developing a laser cooled trapped cesium apparatus with a hydrogen maser fly-wheel oscillator to be flown in a space station where only weak trapping fields will be required to store the atoms for a long time. 7. Laser Cooled Atoms and Ions at Optical Frequencies 2000-... :Higher clock frequencies have always been considered a desirable goal since, for the same phase error, the resulting fractional frequency error is inversely proportional to the clock frequency. Clocks at optical frequencies have been based on absorption spectroscopy and on two-photon spectroscopy employing two laser beams at the same frequency going in opposite directions so that the first-order Doppler shifts cancel [911]. Until recently, however, clocks at optical frequencies required complicated

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16

frequency chains for comparison with lower frequency standards. This situation has dramatically changed in the past two years with the development by Hansch and his associates of a regularly spaced frequency comb of a mode-locked femtosecond laser broadened in a non-linear optical fiber [18]. With this they have measured the 1S-2S transition in atomic hydrogen to 1.8 parts in 1014. This or similar atomic transitions could be used for an accurate atomic clock In an important recently published paper on the ion 199Hg+, Diddams, Bergquist, Drullinger, Itano, Wine land and others [19] have met all the requirements for a successful optical frequency standard, (a) Laser cooling, (b) frequency stabilization of the lasers and (c) the use of femtosecond mode locked lasers combined with nonlinear fibers to provide simple phase-coherent connections between radio and optical frequencies. They have shown that their frequency standard at microwave frequencies is as stable as their comparison hydrogen maser and at optical frequencies the instability is less than 7 x 10"15. References 1. J. C. Maxwell, Treatise (1873). 2. I. I. Rabi. Space quantization in a gyrating magnetic field, Phys. Rev. 51 (1937) 652. 3. I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch, A new method of measuring nuclear magnetic moments, Phys. Rev. 53 (1938) 318. 4. N.F.Ramsey, Molecular Beams. (Oxford Univ. Press, 1956 and 1984) 5. N. F. Ramsey, History of Atomic Clocks, J. Res. NBS 88 (1983) 301.This article contains extensive references to the original publications on the subject. 6. N. F. Ramsey, The method of successive oscillatory fields, Phys. Today 33(7) (1980)25. 7. H. Hellwig, K. M. Evenson, and D. J. Wineland, Time, Frequency and Physical Measurement, Phys. Today 31(12) (1978) 23. 8. N. F. Ramsey, The Atomic Hydrogen Maser, Am. Sci. 56 (1968) 420. 9. F. T. Arecchi, F. Strumia, and H. Walther, eds., Advances in Laser Spectroscopy, (Plenum). 10. T. W. Hansch and Y. R. Shen, eds.,Laser Spectroscopy, vol. 7, (Springer-Verlag, 1985). 11. D.J. Wineland and W. M. Itano, Laser cooling, Physics Today 40(6) (1987) 34. 12. R. S. Van Dyck, Jr., and E. N. Fortson, eds., Atomic Physics, vol. 9, (Singapore: Scientific Publishers, 1984). 13. J. Jesperson and J. Fitz-Randolph, From Sundials to Atomic Clocks (U.S National Bureau of Standards, \911).hk 14. P. D..Lett, W. D, Phillips, et al., Phys Rev Lett 61 (1988) 169.

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17

15. A. Aspect, C. Cohen-Tannoudji, et al., Phys Rev Lett 61 (1988). 16. J. Dalibard, C. Cohen-Tannoudji, et al., Jour. Opt. Soc. Am. B6 (1989) 2023, 2046 and 2112. 17. M. Kasevich, E. Riis, S. Chu and R. S. DeVoe, Phys Rev Lett. 63 (1989) 612 18. J. Reichert, N Niering, R. Holzworth, M. Weitz, Th. Udam and T. W. Hansch, Phs. Rev Lett. 84 ( 2000) 3232. 19. S. A. Diddams, Th. Udem, J. C. Bergquist, E.A. Curtis, R. E. Drullinger, I. Holberg, C.W. Oates, K.R. Vogel.W. Itano, and D. J. Wineland Science 293 (2001) 825

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RELATIVTSTIC Q U A N T U M T H E O R Y OF MICROWAVE A N D OPTICAL ATOMIC CLOCKS

CHRISTIAN J. BORDE Laboratoire de Physique des Lasers, University Paris-Nord, Villetaneuse, and Bureau National de M&trologie, Paris, Prance Tel +33-608221484, Fax +33-608018459, E-mail: chboOccr.jussieu.fr The accuracy of atomic clocks, in the microwave or in the optical domain, is now such that a new theoretical framework [1] is required, which includes: 1 - A fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold atom interferometric devices use atoms in "free fall" in a fountain geometry), 2 - An account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones, 3 - A second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties, 4 - A covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines, is presented, using both an exact propagator of atom waves in gravito-inertial fields [2] and a covariant Dirac equation in the presence of weak gravitational fields [3]. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source can be discussed in the context of present and future microwave and optical clocks.

T h e goal of this paper is t o introduce a unified picture of microwave a n d optical clocks using t h e language of a t o m interferometry. T h e wave character of atoms is getting more a n d more manifest in these devices: t h e recoil energy hS = h2k2/2M is not negligible any more in Cesium clocks {8/u ~ 1.5 1 0 ~ 1 6 ) . Atom sources may now b e coherent sources of matter-waves (atom lasers or atomasers 4 ). We have t o deal with a very different picture from t h a t of small clocks carried by classical point particles. T h e atomic frame of reference may not b e well-defined. Atomic clocks are t h u s now fully q u a n t u m devices in which b o t h t h e internal a n d external degrees of freedom must b e quantized. Finally gravitation a n d inertia play a key role in slow a t o m clocks. T h e Einstein red shift a n d t h e second-order Doppler shift may become important and thus atomic clocks have t o b e t r e a t e d also as relativistic devices. T h e wave properties of a t o m s are fully described by a dispersion law relating t h e de Broglie frequency t o t h e d e Broglie wave vector, which is obtained by t h e introduction of Planck constant in t h e law connecting t h e energy E(jpr) t o t h e m o m e n t u m p . In free space (Figurel): E(~j?) = y/M2c*

18

+ p2c2

19 ENERGY

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-+SQ

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atom slope=v

/

EM WAVE 2 *2

MOMENTUM

Figure 1

Figure 2

We shall make a systematic use of these energy-momentum diagrams t o discuss t h e problem of interaction of two-level atoms with two separate field zones in a Ramsey excitation scheme (Figure 2). Figures 3 and 4 illustrate t h e energy and m o m e n t u m conservation between this two-level a t o m a n d effective photons from each travelling wave in t h e transverse a n d longitudinal directions a n d display t h e recoil energy, t h e first a n d second-order Doppler shifts a n d t h e transit broadening. It is clear from Fig. 4 t h a t , out of resonance, a n additional longitudinal m o m e n t u m is transferred t o t h e a t o m s in t h e excited state.

Recoil enei

Figure 4

Figure 3

For each field zone, we can calculate t h e first-order excited s t a t e transition a m p l i t u d e 3 ' 2 for a Gaussian field envelope (as an example):

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ei(w-a;(,a^feDi-«)(x-x1)/i;Xei[-^(T

-6)2/^l

vx >

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(1) ft

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20 as the product of the e.m. carrier times a Rabi frequency and a Rabi envelope, times an additional momentum phase factor for each initial wave packet Fourier component. This additional longitudinal momentum (Fig.4) is proportional to the detuning and is responsible for the Ramsey fringes, since de Broglie waves associated with each path have a different wavelength in the dark zone11'7 (Fig.2): fd^(-r,t)b^*(-r,t)oc

[dpze~™2(«-"b«Tkv,-6)>/2vl

(2)

eH^-u,ba^kv,-s)(x2-x1yvICa(,o)^a(o),^

This Ramsey interference pattern has a blue recoil shift S and is the superposition of fringe sub-systems corresponding to each velocity class, shifted by the first-order Doppler effect. If the transverse velocity distribution is too broad (absence of diaphragm) or in the optical domain, this will blur out the fringes. To make the connection with atom optics, this superposition can be rewritten as a correlation function involving the degree of coherence of the atom source0: JdzaP\z T ^

(x2 - *i) /vx,t)a^*(z,t)

(3)

Fringes will be obtained as long as hk {x i ) => 8 (p, - p'z ± 2hk)

(4)

The resulting signal exhibit fringes with an opposite recoil shift —8. Unlike the previous one, this signal depends upon the propagation characteristics of the incident atom wave: /'dzbQC?',i)4?"fr*\t) oc dpze-i(±kvI+2S)(2Xo-X2~Xl)/vx

jiv-uf+W**-**)/*. (0) a

{pz)a^,(Pz±2hk)

(5)

/

This integral is easily calculated for Gaussian wave packets and statistical mixtures (a more realistic strong-field numerical approach to this recoil problem is also presented in this book 22 ). If the waist position x$ of the atom wave is not well-defined (e.g. in a thermal beam), energy conservation requires kvz = =F26 and will not be satisfied for most velocities (Fig. 6) and this signal will tend to average out. For a coherent atom wave, if the waist is located at Xi, this second contribution will have the same magnitude as the first one and the overall recoil shift will cancel 22 . If it is focussed at the midpoint XQ = (xi + x |F'=3,mF'=0) transition. The microwaves are introduced through an axial loop antenna inside the vacuum chamber and a subsequent transit of a light sheet removes the remaining F=4 atoms. The microwave cavity and the drift region are enclosed in a highperformance magnetic shield set providing an axial shielding effectiveness of better than 35,000 [3]. An axial solenoid provides a 225 nT magnetic field for the cavity and free precession regions. The entire outer shield and the part of the vacuum chamber that it encloses are held at 44.5+0.1°C. As a result, everything inside the shields, including the microwave cavity, the drift region and the C-field solenoid is temperature-stabilized and gradients are minimized. Making the entire outer shield an isotherm instead of temperature-stabilizing individual components contained therein greatly reduces the sensitivity of this fountain to ambient temperature fluctuations and enhances its robustness for continuous operation. The small magnetic fields generated by the resistive heaters are kept far away from the sensitive drift region. Tests indicate no detectable perturbation to the atoms due to these fields. After making two transits of the microwave cavity, the atoms return to the detection region. Both F=3 and F=4 atoms are detected, allowing us to calculate a transition probability, and reject atom number fluctuations. We typically run the fountain with a cycle time of 1.35 seconds. We originally used square-wave modulation of the interrogation frequency, alternating between ±0.5 Hz from our approximately 1 Hz FWHM resonance. We found that modulating the phase of this synthesizer, leaving its frequency constant, improves the fountain's stability. The phase is changed by ±90° between the two microwave pulses that are part of each interrogation cycle. This approach is insensitive to fluctuations in launch height and is very similar to a scheme being

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82

considered for space-borne cold atom clocks to reduce their sensitivity to vibrations [4]. Our frequency chain is shown in Figure 1. The 9.2 GHz of the Dielectric Resonant Oscillator (DRO) is phase-locked to the 92nd harmonic of the 100 MHz reference input. This output is mixed with the output of a commercial direct digital synthesizer (DDS) to produce the required interrogation frequency. The various sidebands are not suppressed, but the 300 kHz linewidth of our high-Q cavity rejects these with high efficiency. This chain is simple, robust and built entirely from commercially available components. In addition, this topology allows us to insert the digital synthesizer at the top of the chain (instead of at approximately 500 MHz, as had been done previously), removing a multiplicative factor of its contributed noise. While we have not fully characterized this chain yet, it has improved the short-term stability of our fountain and reduced the upper bound on our Dick-effect [5] noise.

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94

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5.

Future Prospects

The demands on frequency flywheels and long-distance frequency-transfer techniques will increase as fountain performance improves and the uncertainties are reduced. Fortunately there are a number of potential improvements on the horizon that should yield better performance. One possible approach to improved frequency stability for the frequency reference (flywheel) is the use of cold-atom standards designed for frequency stability [11] rather than accuracy. Such devices have the potential to deliver reliable signals with short-term frequency stability below lxlO"13 at 1 second, and long-term (up to hundreds of days) stability below lxlO'16. For long-distance transfer of time and frequency there are some areas where the stability of TWSTFT can be improved. For example, no attempt is currently made to correct for small ionospheric effects, and this could be incorporated. Higher chip rates for wider bandwidth spread spectrum would be useful, along with higher data rates (sessions more often than three times per week). Reduced multi-path and improved environmental controls on ground-based equipment would result in improved stability. Also, under some circumstances, the phase of the two-way carrier can be tracked, and this also significantly improves transfer stability [12]. Time and frequency transfer via GPS carrier-phase is still relatively new and it is reasonable to expect improvement in performance through improved software and hardware. Elimination of the slow time difference fluctuations in Fig. 1 (whether it comes from TWSTFT or carrier-phase) would be a significant improvement in itself. Given that there are a number of known areas where improvements can be made it is not unreasonable to expect improvement by a factor of five to ten in the stability of time and frequency transfer techniques over the next decade or so. This would give a frequency-transfer uncertainty significantly better than lxlO"17 at 30 days. Unfortunately, this level of performance has to be achieved in at least two independent transfer techniques in order to be confident of the performance.

6. Summary With current technologies frequency comparisons involving displacements in time or space can usually be made in a reasonable time with added uncertainties well under lxlO"15. This is adequate for present-day cesium fountains, but as cold-atom technologies improve this will no longer be sufficient. More stable flywheels will be needed along with long-distance frequency-transfer techniques of higher stability. Fortunately, better comparison technologies are on the horizon.

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References 1. Parker T. E., Proc. 1999 Joint Meeting of the European Freq. and Time Forum and the IEEE International Freq. Control Symp., pp. 173-176, 1999. 2. Douglas R. J. and Boulanger J. S., Proc. IIth European Freq. and Time Forum, pp. 345-349,1997. 3. Parker T. E. et al, Proc. 15th European Freq. and Time Forum, pp. 57-61, 2001. 4. Parker T. E., Proc. IEEE International Freq. Control Symp., pp 57-62, 2001. 5. Kirchner D., Proc. of the IEEE, vol. 79, pp. 983-990, 1991. 6. Larson K. M. and Levine J., IEEE Trans, on Ultrason., Ferroelect., and Freq. Contr., vol. 46, no. 4, pp. 1001-1012, 1999. 7. Lewandowski W. and Thomas C , Proc. of the IEEE, vol. 79, pp. 991-1000, 1991. 8. Nelson L., Levine J. and Hetzel P., Proc. 2000 IEEE International Freq. Control Symp., pp. 622-628, 2000. 9. Parker T. E., Howe D. A., and Weiss M., Proc. 1998 IEEE International Freq. Control Symp., pp. 265-272, 1998. 10. Parker T. E. et al, Proc. IEEE International Freq. Control Symp., pp 63-68, 2001. 11. Jefferts S. R. et al , "Proposed laser-cooled 87 rubidium local oscillator at NIST", in this proceedings. 12. Schafer W., Pawlitzki A. and Kuhn T. Proc. 31s' Annual Precise Time and Time Interval Meeting, pp. 505-514, 1999.

Acknowledgements The author would like to thank Peter Hetzel, Stefan Weyers, and Andreas Bauch at PTB for their invaluable help in making the fountain comparison. Also, the author thanks Steve Jefferts and Tom Heavner for the NIST-F1 evaluations, Lisa Nelson and Judah Levine for the carrier-phase data, and Trudi Peppier and Victor Zhang for help with the two-way data.

U.S. Government work not protected by U.S. copyright

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Part IV

Trapped Ions I

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A MERCURY-ION OPTICAL CLOCK*

J.C. BERGQUIST, U. TANAKA, R.E. DRULLINGER, W.M. ITANO, D.J. WINELAND, S.A. DIDDAMS, L. HOLLBERG, E.A. CURTIS, AND C.W. OATES National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3328, USA e-mail: [email protected]. eov TH. UDEM Max-Planck-Institute fur Quantenoptik 85748 Garching, Germany We have developed an optical clock based on a laser whose frequency is locked to a single, laser-cooled 199Hg+ ion and that uses a femtosecond laser and raicrostructure fiber to phasecoherently divide the optical frequency to a countable microwave frequency. The measured short-term stability in the optical domain is about an order of magnitude higher than the best cesium-fountain clock. The estimated value of the electric-quadrupole frequency shift of the 2 Si/2 (F = 0, mF= 0) - 2D5/j (F = 2, mF= 0) clock transition is given.

1. Introduction An important measure of the performance of an atomic clock is the frequency stability of its locked reference oscillator. For a given linewidth and atom number, the stability of an oscillator that is steered to resonance with an atomic transition is directly proportional to the frequency of the oscillator. Hence, a clock operating at a frequency in the optical region of the electromagnetic spectrum (= 1015 Hz) could be niany orders of magnitude more stable than clocks operating at a frequency in the microwave region of the spectrum (= 1010 Hz). In fact, it is possible to exchange some of the potential gain in stability for higher accuracy by using only a small number of atoms that are confined to a small volume in space. However, only recently has there been a practical device that is capable of faithfully "counting" each cycle of the optical radiation in order to generate time. In these Proceedings (see also the contributions by E. Curtis et al. and S. Diddams et al), we report on research at NIST toward the realization of highly stable and accurate optical timepieces [1] that use a femtosecond laser and a microstructure fiber as the "clockwork" to phase-coherently divide down the optical frequency to a countable microwave frequency [2-9]. Here, we concentrate on the description of the mercury optical standard, where the frequency of an optical oscillator is short-term stabilized by locking to the resonance of a high-finesse cavity [10] and long-term stabilized by locking its harmonic to the narrow resonance of the 2 S 1 / 2 (F = 0, m F = 0) - 2 D 5 / 2 (F =

99

100

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2, mp = 0) electric-quadrupole-allowed transition (282 nm or 1.064 PHz) of a single, laser-cooled 199Hg+ ion [11]. This system has demonstrated better stability (and anticipates higher accuracy) than that of the microwave cesium-fountain standards [1,11]. We describe its present and anticipated performance, and briefly present its main limitation. 2. Stability of atomic clocks The Allan deviation Oy(x) provides a convenient measure of the fractional frequency instability of a clock as a function of averaging time T [12]. For an oscillator locked to an atomic transition of frequency f0 and linewidth A/,

where A/,™ is the measured frequency fluctuation, N is the number of atoms, and T is the cycle time (the time required to make a single determination of the line center) with T > T. This expression assumes that technical noise is reduced to a sufficiently small level such that the quantum-mechanical atomic projection noise is the dominant stability limit [13,14] and that the signal contrast is 100 %. If we further assume that the signal linewidth A/ = 1/2T (i.e., Ramsey interrogation and zero dead time), then [15]

a

^~~W^-

(2)

In both cases, the fractional frequency instability increases if the signal contrast is less than 100 %, which could be caused, for example, by technical noise that is comparable to, or greater than the quantum projection noise, or a laser linewidth that exceeds the inverse probe time. The contrast can also be degraded if the ion is not strongly confined in the Lamb-Dicke limit where the average quantumoccupation number < 1 [16]. If > 1, then fluctuations in n from measurement cycle to measurement cycle can cause variations in the transition probability of the ion [17], which reduce the signal contrast. The signal contrast and clock stability is also fundamentally diminished as the probe period approaches the natural lifetime t D of the metastable state. In this case, the signal strength decreases because the ion can decay during the probe and detection period. A quantitative treatment that includes decay shows that the optimum probe time to minimize ay(f) for Ramsey excitation is nominally the same as the metastable lifetime [18]. For this case, ay(T) is degraded by nearly a factor 2 compared to the case of an equivalent probe time without atomic decay. Thus,

101

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assuming zero dead time and < 1, the optimum stability is approximately given by

WTM

•

F+l (where F = I = 9/2) with circularly polarised light in zero magnetic field results via optical pumping between the Zeeman sublevels in a closed two-level system. The laser radiation is produced using a frequency-doubled stilbene-3 ring dye-laser. The laser is frequencystabilised to a reference cavity by use of a high bandwidth electronic servo system, resulting in a laser linewidth below 10 kHz. To provide faster cooling at higher temperatures and, furthermore, be able to record high-resolution spectra of the cooling transition in the Lamb-Dicke regime, we use a bichromatic cooling method [12]. For that purpose the laser is passed through an electro-optical modulator with variable modulation frequency. Through

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110

phase modulation two weak sidebands containing each about 0.1 % of the laser power are created around the original laser frequency. The carrier frequency of the laser is detuned by about - 40 MHz from the cooling transition resonance and efficiently cools the ion from higher vibrational levels, when these get excited, e.g. by collisions with the residual gas. The high frequency phase modulation sideband is used - when tuned to the first red secular sideband - to cool the ion close to the quantum ground state. It can also be scanned over the carrier frequency by changing the drive frequency of the electro-optical modulator.

/ f «* - w • • ^ • • ' • • ^ - • , s • ^

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- 2 - 1 0 1 2 3 detuning of laser sideband [MHz]

Figure 3. Excitation spectrum of the cooling transition of a single In+ ion obtained with bichromatic sideband cooling (averaged over 32 scans). The lower curve shows the deviation of the measured data points from the fitted Lorentzian curve in tenfold magnification.

An excitation spectrum obtained this way is shown in Fig. 3. The spectrum is dominated by the carrier and the excitation of red secular sidebands is very weak as can be seen from the magnified deviations between the data and a fitted single Lorentzian curve. In the region of laser detunings corresponding to the red vibrational sidebands an increase of the signal by about 2 (1) % of the height of the center Lorentzian is observable. In the Lamb-Dicke limit the height of the first red sideband relative to the carrier is given by k2 x02 where k is the wavenumber of the cooling laser light and x0 the extension of the ground state wavefunction. As in the bichromatic cooling scheme the ion always remain in the Lamb-Dicke regime [12], we can determine from the ratio of red secular sideband amplitude to carrier amplitude a mean vibrational quantum number = 0.7 (3), corresponding to a temperature of 60 nK. This result indicates that the ion is in the vibrational ground state with a probability exceeding 50 % for a basically unlimited amount of time.

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3. High-resolution spectroscopy and absolute frequency measurements Spectroscopy of the narrow 'S 0 —> 3Po clock transition is performed in opticaloptical double resonance [1]. An excitation of the metastable 3 P 0 level leads to a dark period in the single ion fluorescence signal on the cooling transition until the state decays or the valence electron is brought back to the ground state by a stimulated process. In this way absorption of one clock transition photon prevents subsequent scattering of some 105 or 106 fluorescence photons of the cooling transition and thus allows detection of a transition to the metastable state with practically 100 % efficiency. The laser system used for excitation of the lS0 —> 3Po resonance is described in [15]. It consists of a diode pumped Nd:YAG laser emitting at 946 ran. This laser is frequency-stabilized to a passive resonator of high finesse. A second diode pumped Nd:YAG laser is used for power amplification and efficient generation of the second harmonic at 473 nm. Infrared light from the stable master laser is coupled into this laser to transfer the frequency stability via injection locking. The blue light is coupled into an enhancement cavity to generate the UV radiation at 237 nm using a BBO crystal. In order to obtain high-resolution spectra of the clock transition any light-shift and broadening of this transition by the cooling laser has to be avoided [16]. Both laser beams are therefore applied alternately in time and blocked by means of mechanical shutters. A high resolution spectrum of the clock transition is shown

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112

in Fig. 4. The clock laser power was reduced to 30 nW to avoid saturation broadening. Typically, the clock laser frequency is changed in steps of 8 Hz and four attempts are made at each frequency. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution of Av/v = 1.3 x 10"13 [9]. A spectral window of 200 Hz contains 50 % of all excitations. According to the experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the ion is expected beyond a level of 1 Hz. The linewidth obtained is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian but reflects the fluctuations of the laser frequency, that arise mainly at low modulation frequencies in the range 1-15 Hz. A measurement of the frequency stability of the laser using a second independent reference cavity gives a consistent result. We currently work on the improvement of the clock-laser frequency stability. Using a quasimonolithic Nd:YAG ring-laser [17], mounted on an active vibration isolation platform, recently lead to laser linewidths below 6 Hz over integration times of up to 26 s [18]. >Jj 2000

3] 1500 NO

— 1000 C\ ON

3 0,04

§S

500

§

-500

rJ-1000 +A-1500

;V -» |3P0 , 9/2, 7/2> component using o" polarized light, we were able to determine the Zeeman shift to 636 (27) Hz/G [9]. To obtain the anticipated uncertainty of 1 mHz, control of the magnetic field with a precision of a few \iG is required. As the ion can be localized to a small fraction of the wavelength of the clock transition, a recoil-free and Doppler-free carrier is obtained. The second order Doppler shift is proportional to the temperature and is below 1 mHz for temperatures T < 1 mK. Electric fields lead to a quadratic Stark shift of the transition frequency. In positive ions the static polarizabilities are generally smaller than in neutral atoms because the valence electrons are more tightly bound. By comparison with the Cd atom, which is isoelectronic to In+, we estimate the quadratic Stark shift of the indium clock transition to be below 1 mHz/(V/cm)2. The Stark shift introduced by the trap field is proportional to the mean quadratic distance from the trap center and therefore proportional to the temperature of the ion. The shift is smaller than 0.1 Hz/K for our typical trap conditions and therefore negligible at the sub-mK temperatures achievable with laser cooling. The electric field gradient of the trap has no influence, since both levels of the clock transition have a vanishing quadrupole moment. The influence of the thermal radiation can be estimated using static polarizabilities. At a trap temperature of 300 K, control of the temperature to ± 1 K will be found sufficient to reduce the uncertainty in the black-

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body shift below 1 mHz. The combination of the very small systematic uncertainties in the transition frequency of the trapped indium ion and the availability of the technically convenient Nd:YAG laser to drive this transition makes this ion a most promising candidate for a future optical clock. Acknowledgements We gratefully acknowledge the collaboration with R. Holzwarth, P. Pokasov, J. Reichert, Th. Udem, Th. Hansch and S. N. Bagayev in the absolute optical frequency measurement. References [I] Dehmelt H., IEEE Trans, lustrum. Meas. 31 (1982), 83. [2] Rafac R. J. et al., Phys. Rev. Lett. 85 (2000), 2462. [3] Tamm C , Engelke D. and Buhner V., Phys. Rev. A 61 (2000), 053405. [4] Stenger J. et al., Opt. Lett. 26 (2001), 1589. [5] Yu R , Zhao X., Dehmelt H., Nagourney W., Phys. Rev. A 50 (1994), 2738. [6] Bernard J. E., Marmet L. and Madej A., Opt. Comm. 150 (1998), 170. [7] Nagerl H. C. et al., Phys. Rev. A 61 (2000), 023405. [8] Peik E., Hollemann G. and Walther H., Phys. Rev. A 49 (1994), 402. [9] Becker Th. et al., Phys. Rev. A 63 (2001), 051802. [10] Wineland D. and Dehmelt H., Bull. Am. Phys. Soc. 20 (1975), 637. [II] Diedrich F. et al., Phys. Rev. Lett. 62 (1989), 403. [12] Peik E. et al., Phys. Rev. A 60 (1999), 439. [13] Yu N., Nagourney W. and Dehmelt H., /. Appl. Phys. 69 (1991), 3779. [14] Schrama C. et al., Opt Comm. 101 (1993), 32. [15] Hollemann G. et al., Opt. Lett. 20 (1995), 1871. [16] Arecchi F. T. et al., Phys. Rev. A 33 (1986), 2124. [17] Freitag I. et al., Opt. Lett. 20 (1995), 2499. [18] See the contribution by Nevsky A. Yu. et. al. in these proceedings. [19] von Zanthier J. et al., Opt. Comm. 166 (1999), 57. [20] von Zanthier J., Opt. Lett. 25 (2000), 1729. [21] Bagayev S. N., Dimitriyev A. K., Pokasov P. V., Laser Phys. 7 (1997), 989. [22] Reichert J. et al., Phys. Rev. Lett. 84 (2000), 3232; Diddams S. A. et al., Phys. Rev. Lett. 84 (2000), 5102. [23] Becker Th. et al., in The Hydrogen Atom, eds. Karshenboim S. G., Pavone F., Bassani F., Inguscio M., Hansch T. W. (Springer, Berlin, 2001), 545.

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A FREQUENCY STANDARD USING THE 2 S 1 / 2 - 2 F OCTUPOLE T R A N S I T I O N IN 171Yb+. S. A. W E B S T E R , P. TAYLOR, M. ROBERTS, G. P. BARWOOD, P. BLYTHE AND P. GILL National Physical Laboratory, Teddington, Middlesex, TW11 OLW, UK. E-mail: [email protected] The 2Si/2-iFi/2 octupole transition in m Y b + is probed using the quantum jump technique and a spectrum of the carrier on the (F = 0, mp = 0)-(F = 3, TTIF = 0) component is observed with linewidth of 4.5kHz. Measurements are made of the second-order Zeeman shift and the AC Stark shift for this transition and show good agreement with theory.

1

Introduction

A high Q optical transition in a single trapped ion has the potential to be a frequency reference of unprecedented stability and accuracy 1 and the recent advances in laser stabilisation 2 and optical frequency measurement 3 have now made possible the goal of an optical clock 4 . Investigations are underway into several ion species with forbidden transitions in their optical spectra 5 ' 6 , 7 , 8 . The 1 7 1 Y b + system has several such transitions, 2 S 1 / 2 - 2 D 3 / 2 , 2 S i / 2 - 2 D 5 / 2 , and 2 F 7 / 2 - 2 D 5 / 2 , as well as the ground state microwave transition, 2 S ] / 2 ( F = 0 - F = 1 ) , all of which m a y b e considered for frequency standards 7 , 1 0 , 1 1 ' 1 3 (see fig. l a for the term scheme). The 1 7 1 Y b + ion also has the advantage of having in its atomic structure Zeeman sublevels with mp = 0, allowing for transitions which are insensitive to magnetic fields to first order. At NPL we are working on the 2 S i / 2 - 2 F 7 / 2 electric octupole transition, where the metastable 2 F7/ 2 state is extremely long lived, with an estimated lifetime of 10 years 9 . Consequently, the transition width is on the order of nHz and poses no practical limit to the time for which ion may be interrogated. Given that the current state-of-the-art laser linewidth is 0.2Hz 2 , this opens up the possibility of stabilities at the part in 10 18 level, achievable with an averaging time of just a few hours. Location of the transition was aided by spectroscopy on the 2 S 1 / 2 - 2 D 5 / 2 1 0 2 and F 7 / 2 - 2 D 5 / 2 n transitions, the difference in their frequencies providing an estimate of the 2 Siy 2 - 2 F7/2 transition frequency. After repeatedly scanning the frequency of a probe laser around this region of interest, a total of 14 quantum jumps to the F state were observed in an interrogation time of

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116

7680s and this was sufficient to locate the transition to within 0.8MHz12. Since this first experiment, improvements have been made to the probe laser system, with the implementation of frequency stabilisation to an ultrahigh finesse Fabry-Perot etalon. The linewidth of the probe laser has been reduced to 4.5 kHz, determined from the spectrum of the octupole transition (section 3) and the rate of quantum jumps on line centre is now 0.5 s - 1 . With this linewidth, it has been possible to resolve systematic shifts to the transition frequency, namely the second-order Zeeman shift and the AC Stark shift. A theoretical treatment of these shifts along with the experimental determination of their size is presented in section 4. 2

Experimental setup a)

b)

Figure 1. Term scheme of

m

Y6+ and experimental setup.

A schematic of the experimental setup is shown in figure lb. An endcaptrap 15 is used with an electrode separation of 0.56 mm, a drive frequency of 12.8 MHz and peak voltage of 290 V. Laser cooling is performed on the 2 S 1 / 2 (F=l) _ 2 Pi/2(F=0) transition (see fig. la), the radiation at 369nm being generated by a frequency doubled TkSapphire laser. Due to the possibility

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117

of decay from the 2 P 1 / 2 (F=0) state to the 2 D 3 / 2 (F=1) state, a repumper at 935 nm is employed exciting the ion to the 3 D[3/2] 1 / 2 (F=0) state from where it decays back to the 2 Si/2(F=l) ground state. The radiation at 935 nm is generated by an external cavity diode laser. There is a finite probability of a spontaneous Raman process from the 2 Si/ 2 (F=l) state to the 2 Si/ 2 (F=0) state via the 2 P 1( / 2 (F=1) state, therefore a microwave repumper at 12.6 GHz is also employed to maintain the cooling cycle. Light at 467nm for probing the 2 S!/ 2 - 2 F7/ 2 transition is generated by frequency doubling a Ti:Sapphire laser at 934 nm which is stabilised to an ultra-high finesse Fabry-Perot etalon [T ~ 250000) made from ultra-low expansivity glass. Frequency stabilisation is done using a Pound-Drever-Hall scheme14 with feedback to an AOM, external to the laser cavity. In order to achieve the highest servo bandwidth, the light is made to come to a focus in the AOM crystal and passes as close to the piezo transducer as possible. This minimizes the time delay due to the transit time of the accoustic wave to the laser beam and a bandwidth of w 350 kHz is achieved. An additional AOM spans an offset of -246 MHz, between the atomic transition and the nearest TEMoo mode of the etalon. After frequency stabilisation, the light is critically phase-matched in a 7mm-long, ab-cut crystal of KNb03, generating 25 mW at 467 nm. Due to the weakness of the octupole transition, the probe beam must have as high an intensity as possible, therefore it is focused to a 5 pm spot at the position of the ion. The probe laser is aligned on to the ion using a tracer beam of cooling radiation (369 nm) which is also focused to a 5 /im spot by the achromatic lens system. First the tracer is aligned on the ion by maximizing the fluorescence emitted from the ion. The fluorescence is detected by a photomultiplier tube after collection by a large aperture lens. Secondly, the probe beam is aligned to be co-linear with the tracer over a 5 m beam path, using multi-pass mirrors, then the foci are made coincident, by simultaneously maximizing the transmission of each beam through a 5 pm pinhole at the focus. The transition is probed using the quantum jump technique1 in which the cooling and probe beams are switched in anti-phase and a transition to the metastable state is detected by the absence of fluorescence on the cooling transition. A second cooling beam with a weaker focus is used for this stage of the experiment and is switched using an AOM. The probe beam is switched using a shutter. The durations of the cooling and probe pulses are 300 ms and 330 ms respectively. In order to prepare the ion in the 2 Si/ 2 (F=0) state before probing, the microwave repumper is switched off 60 ms before the cooling beam is switched off. A magnetic field of 300 fiT is applied to prevent optical

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118 pumping to dark states on the cooling transition, and its direction is chosen to preferentially select the mF=0-mF= ; 0 transition (60% of the total transition probability). By stepping the frequency of the AOM bridging the offset to the etalon, the probe laser is made to scan over the transition. From successive scans a histogram of quantum jumps is built up (see fig. 2). Once a jump to the F state has been detected, the ion is excited to the 1 D[5/2] 6 ^ 2 state with radiation at 638 nm, from where it decays back to the ground state via the D-states. This light is generated by an extended cavity diode laser and is switched using an AOM. 3

Spectroscopy of the 'Swa— 2 F 7 / 2 transition.

-10

-8

-6

-4

-2

0

2

4

6

Frequency oflsetfromline centre (kHz)

Figure 2. Spectrum of the 2 Si/a(F = 0,mp = 0)- 2 F 7 / 2 (F = 3,mF = 0) transition. Figure 2 shows a quantum jump spectrum of the carrier for the Si/2{F = 0,m,F — 0)-2F7/2(F = 3,mF - 0) transition. The data is a collation of 10 scans across the feature, each consisting of 25 steps of 400 Hz, with 10 probe interrogations at each step. In order to take out the frequency drift of the etalon throughout the experiment, a fit was made to the mean frequency of each scan as a function of time, and the change in frequency relative t o the first scan subtracted from each data set. The linewidth of the feature (FWHM) is 4.5(2) kHz and the jump rate on line centre was 0.5 s - 1 . 2

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The probe intensity during the scans was set so that the probability of exciting a transition in the interrogation time was well below 50%. 4 4-1

S y s t e m a t i c Frequency shifts Second order Zeeman shift

The levels involved in the measured transition have M F — 0 and are therefore free from the linear Zeeman effect. However, a second order perturbation from a magnetic field, B, gives rise to the shift HB9J,2^\(F'M\JZ\FM)\>2

A,z2 = - ( ^ ) 2 E

Epi — Ep

where it has been assumed that the magnetic field defines the quantization axis, z. The square of the matrix element can be expressed in terms of Wigner 3j and 6j symbols as \{F'M\J2\FM)\2

= 1(1 + 1)(2I + 1)(2F + 1)(2F' + 1)

/ F lF'V * \-M0Mj

2 c

7-1 iV2 f I F JV \F' I 1 / T

For both the S and F states, the only term that needs to be considered in the sum is that due to the nearest hypernne level, thus the denominator is given by the hyperfine splitting. The shift of the 2 S 1 / 2 ( F = 0, mp = 0) state is therefore A f z 2 ( S ) = —15.49 mHz(//T) - 2 , where the matrix element is equal to 5, 9j = 2 and the hyperfine splitting, A.isHFS = 12.643 GHz 13 . The shift of the 2 F 7 / 2 ( F = 3,m F = 0) state is Ai/ Z 2 (F) = - 1 7 . 6 2 ( l ) m H z ( p T ) - 2 , where the matrix element is equal to | , gj — | and AI/HFS = 3.620(2) GHz 1 1 . Taking the difference between these two values, the shift of the 2 S i / 2 - 2 F 7 / 2 transition is predicted to be A i / Z 2 ( 5 - F) = 2.12(1) mHz(//T)- 2 . Scans were taken over the transition for a range of magnetic fields and the shift in the mean frequency relative to the frequency at zero field is plotted against the square of magnetic field in figure 3a). The field was calibrated from the splitting of the Zeeman components on the ground state hyperfine transition, observed in the microwave spectrum. The fit gives a measured shift of A f z 2 ( S - . F ) = -1.9(3) mHz(/!/r) - 2 , in good agreement with the predicted value. The lcr uncertainty comprises a 10 % statistical error from the fit and a 13 % systematic error from the calibration of the magnetic field. Currently a field of 300 pT is used to prevent population trapping on the cooling transition. However, it should be possible to work at much smaller fields with the implementation of polarisation spinning 16 or by switching the

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magnetic field to a low value during probing. In a field of 1.5 f/T the shift will be of order 1 part in 1017 with a much smaller uncertainty.

Intensity (10s W m )

B2(mT)2

1.0

12

Figure 3. Plot of (a) second-order Zeeman shift against the square of magnetic field and (b) AC Stark shift against probe laser intensity.

4.2 AC Stark shift The AC Stark shift arises from a second order interaction of the electric field of the probe light with the electric dipole moment, d, induced in the ion by the electric field. The shift is significant for the octupole transition due to the high intensity required to probe it. In a light field, E — EQ cos(wit), the shift is given by17 KylJFMldzlj'IJ'F'M)? &VACStark

= ~

2h

EyiJ'F'M

y'J'F'

— E-yUFM — h^L

\(-yIJFM\dz\-y'IJ'F'M)\

+E y / J ' F ' M n(E2} h2

— ^iIJFM

^

E

-Y'J'F'

2 1

+ hWL.

2u\{-/IJFM\dz\'y'IJ'F'M)\2 or - wt

The states considered are those which are connected to the S or F state by a dipole transition. Rotating and anti-rotating terms have been taken into account because the probe light is in all cases far off-resonant from these transitions. It is assumed that the electric field defines the quantization axis,

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2. The matrix element can be expressed in terms of a weighted oscillator strength and Wigner 3j and 6j symbols, so the shift becomes

A

"— = - i S r jE, whs (2F+wF'+» ( F lF'V * \-M0MJ

f J I F\2 \F'l J'j •

The weighted oscillator strengths used were those calculated by Biemont et oi.18. The contributions from transitions with gf > 0.01 were included in the sum, 15 in total for the S state and 58 for the F state. Given that the intensity is expressed as ce0{E2), the shift of the 2 Si/ 2 (F = 0,mp = 0) state is &VACStark{S) = -515.1 pHzW" 1 m 2 , and for the 2 F 7 / 2 (F = 3,m F = 0) state, &VACStark(F) = —467.7 pHzW _ 1 m 2 . Taking the difference between these two values, the shift of the 2 5 1 / 2 _2 ^7/2 transition is predicted to be &VACStark(S

- F) = 47

M Hz

W"1 m2.

Scans were taken over the transition for a range of intensities and the shift in the mean frequency relative to the frequency at zero intensity is plotted against intensity in figure 3b. The fit gives a measured shift of &VACStark = 421J2,/iHzW_1m2, in good agreement with the predicted value and providing a critical test of the theory of Biemont et al. The lcr uncertainty comprises a 12 % statistical error from the fit and systematic errors due to uncertainty in the spot size (1/e radius 6.5(7)/um horizontally, 4.1(2)/im vertically), uncertainty in the overlap of the probe beam with the 369nm tracer (5%), and uncertainty in the alignment of the tracer on the ion (14%). Currently, with a laser linewidth of 4.5 kHz, an intensity ~ 107 Wm - 2 excites the ion to the F state with 50% probability using a probe pulse length of 330 ms, and this gives a light shift of « 500 Hz. With a laser linewidth of 0.5Hz (the narrowest linewidth reported to date is 0.2Hze), a factor of 104 less intensity would be needed to drive the transition at the same rate, giving a light shift of » 50 mHz or 1 part in 1016. The uncertainty in the shift is large because the tight focus required to generate high intensities leads to large uncertainties in the spot size and alignment accuracy. However, for lower intensities, a larger spot could be used and the uncertainty would be reduced. With active stabilization of power, it is reasonable to expect that intensity and hence the shift could be characterized to the percent level.

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5

Conclusion

The 2 S 1 / / 2 - 2 F7/ 2 octupole transition in m Y b + has been shown to be a viable prospect as a frequency standard with the demonstration of a probe linewidth of 4.5 kHz and a quantum jump rate of 0.5 s _ 1 . Two of the systematic shifts for the system, the second order Zeeman shift and the AC Stark shift, have been measured and are in good agreement with theory. Projections of these shifts, under the likely operating conditions of the standard, indicate that the second-order Zeeman shift will have negligible uncertainty, and the AC Stark shift, although significant, should have an uncertainty approaching the part in 10 18 level. A preliminary measurement of the absolute transition frequency using a self-referenced mode-locked Ti:Sapphire laser has been made 1 9 and work is underway to address the issue of vibration isolation of the ultra-high finesse etalon. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

H Dehmelt, IEEE Trans. Instrum. Meas. 31, 83 (1982). B.C. Young et al, Phys. Rev. Lett. 82, 3799 (1999). S.A. Diddams et al, Phys. Rev. Lett. 84, 5102 (2000). S.A. Diddams et al, Science 293, 825 (2001). R.J. Rafac et al, Phys. Rev. Lett. 85, 2462 (2000). J. von Zanthier et al, Opt. Comm. 166, 57 (1999). Chr. Tamm et al, Phys. Rev. A 61, 053405 (2000). G.P. Barwood et al, Phys. Rev. A 59, R3178 (1999). M. Roberts et al, Phys. Rev. Lett. 78, 1876 (1997). M. Roberts et al, Phys. Rev. A 60, 2867 (1999). P Taylor et al, Phys. Rev. A 60, 2829 (1999). M. Roberts et al, Phys. Rev. A 60, 020501R (2000). P.T.H. Fisk et al, IEEE Trans. Ultrason. Ferroelecr. Preq. Control 44, 344 (1997). R.W.P. Drever et al, App. Phys. B 3 1 , 97 (1983). C.A. Schrama et al, Opt. Comm. 101, 32 (1993). D J Berkland et al, Phys. Rev. Lett. 80, 2089 (1998). B.W. Shore, The Theory of Coherent Atomic Excitation, (Wiley, New York, 1990). E. Biemont et al, Phys. Rev. Lett. 8 1 , 3345 (1998). See S.N. Lea et al, these proceedings.

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PartV

Optical Combs I

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OPTICAL FREQUENCY SYNTHESIS WITH ULTRASHORT PULSES T H . U D E M , R. HOLZWARTH, M. ZIMMERMANN, AND T. W . H A N S C H Max-Planck

Institut fur Quantenoptik, 85748 Garching, E-mail: [email protected]

Germany

Femtosecond laser frequency comb techniques are vastly simplifying the art of measuring the frequency of light. A single mode-locked femtosecond laser is now sufficient to synthesize hundreds of thousands of evenly spaced spectral lines, spanning much of the visible and near infrared region. The mode frequencies are absolutely known in terms of the pulse repetition rate and the carrier-envelope phase slippage rate, which are both accessible to radio frequency counters. Such a universal optical frequency comb synthesizer can serve as a clockwork in atomic clocks, based on atoms, ions or molecules oscillating at optical frequencies.

1

Introduction

For more than a century, precise optical spectroscopy of atoms and molecules has played a central role in the discovery of the laws of quantum physics, in the determination of fundamental constants, and in the realization of standards for time, frequency, and length. The advent of highly monochromatic tunable lasers and techniques for nonlinear Doppler-free spectroscopy in the early seventies had a dramatic impact on the field of precision spectroscopy 1 , 2 . Today, we are able to observe extremely narrow optical resonances in cold atoms or single trapped ions, with resolutions ranging from 1 0 - 1 3 to 1 0 - 1 5 , so that it might ultimately become possible to measure the line center of such a resonance to a few parts in 10 1 8 . Laboratory experiments searching for slow changes of fundamental constants would then reach unprecedented sensitivity. A laser locked to a narrow optical resonance can serve as a highly stable oscillator for an all-optical atomic clock 3 ' 4 ' 5 that can satisfy the growing demands of optical frequency metrology, fiber optical telecommunication, or navigation. However, until recently there was no reliable optical "clockwork" available that could count optical frequencies of hundreds of THz. Most spectroscopic experiments still rely on a measurement of optical wavelengths rather than frequencies. Unavoidable geometric wavefront distortions have so far made it impossible to exceed an accuracy of a few parts in 10 10 with a laboratory-sized wavelength interferometer. To measure optical frequencies, only a few harmonic laser frequency chains have been built during the past 30 years which start with a cesium atomic clock and generate higher and higher harmonics in nonlinear diode mixers, crystals, and other nonlinear

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126 devices 6 , 7 , 8 ' 9 . Phase-locked transfer oscillators are needed after each step, so that such a chain traversing a vast region of the electromagnetic spectrum becomes highly complex, large, and delicate, and requires substantial resources and heroic efforts to build and operate. Most harmonic laser frequency chains are designed to measure just one single optical frequency. In 1998, our laboratory has introduced a revolutionary new approach that vastly simplifies optical frequency measurements. We could demonstrate that the broad comb of modes of a mode-locked femtosecond laser can be used as a precise ruler in frequency space 1 0 , 1 1 . This work has now culminated in a compact and reliable all-solid-state frequency "chain" which is actually not really a chain any more but requires just a single mode-locked laser 1 2 , 1 3 , 1 4 , 1 5 , 1 6 . As a universal optical frequency comb synthesizer it provides the long missing simple link between optical and microwave frequencies. For the first time, small scale spectroscopy laboratories have now access to the ability to measure or synthesize any optical frequency with extreme precision. Femtosecond frequency comb techniques have since begun to rapidly gain widespread use, with precision measurements in Cs 1 0 , Ca 1 7 , 1 8 , 1 9 , 2 0 , CH 4 2 1 , H 2 2 , Hg+ 1 7 , 4 , 5 , I 13,23,24,25,26,27 Y b + 2 8 , 2 9 , 2 7 S r + 2 7 , 3 0 and In+ 3 1 , 3 2 The same femtosecond frequency comb techniques are also opening new frontiers in ultrafast physics. Control of the phase evolution of few cycle light pulses, as recently demonstrated 1 4 ' 3 3 , provides a powerful new tool for the study of highly nonlinear phenomena that should depend on the phase of the carrier wave relative to the pulse envelope, such as above threshold ionization, strong field photoemission, or the generation of soft x-ray attosecond pulses by high harmonic generation. In the first experiment of its kind, we have applied the frequency comb of a mode-locked femtosecond laser to measure the frequency of the cesium Dj line 1 0 . This frequency provides an important link for a new determination of the fine structure constant 3 4 a. More recently, we have measured the absolute frequency of the hydrogen 1S-2S two-photon resonance in a direct comparison with a cesium atomic fountain clock to within 1.9 parts in 10 1 4 , thus realizing one of the most accurate measurement of an optical frequency to date 1 7 ' 5 , 2 9 . During the past few years, precision spectroscopy of hydrogen has yielded a value for the Rydberg constant that is now one of the most accurately known fundamental constant 3 5 . Nonetheless, after more than a century of spectroscopic experiments, the hydrogen atom still holds substantial challenges and opportunities for further dramatic advances.

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2

O p t i c a l F r e q u e n c y Differences

While it has been extremely difficult in the past to measure an absolute optical frequency, a small frequency difference or gap between two laser frequencies can be measured rather simply by superimposing the two laser beams on a photodetector and monitoring a beat signal. The first experiments of this kind date back to the advent of cw He-Ne-lasers in the early sixties 36 . Modern commercial fast photodiodes and microwave frequency counters make it possible to directly count frequency differences up to the order of 100 GHz. Since the gap between the high frequency endpoint of a traditional harmonic laser frequency chain and an unknown optical frequency can easily amount to tens or hundreds of THz, there has long been a strong interest in methods for measuring much larger optical frequency differences. Motivated by such problems in precision spectroscopy of atomic hydrogen, we have previously introduced a general, although perhaps not very elegant solution for the measurement of large optical frequency gaps with the invention of the optical frequency interval divider (OFID) which can divide an arbitrarily large frequency difference by a factor of precisely two 3 7 ' 3 8 . An OFID receives two input laser frequencies / i and / 2 . The sum frequency A + ii and the second harmonic of a third laser 2 / 3 are created in nonlinear crystals. The radio frequency beat signal between them at 2/3 — (/1 + $2) is used to phase-lock the third laser at the exact midpoint. With a divider chain of n cascaded OFIDs, the original frequency gap can be divided by a factor of 2™. To measure an absolute optical frequency rather than a frequency gap the determination of the interval between the laser frequency / and its own second harmonic 2 / was suggested 37 : / = 2 / — / . Frequency intervals up to several THz can also be measured with passive optical frequency comb generators 3 9 , 4 0 . These devices where then proposed to significantly shorten an OFID chain of the 2 / - / type 4 1 . 3

F e m t o s e c o n d Light P u l s e s

The periodic pulse train of a mode-locked laser can be described in the frequency domain as a comb of equidistant modes, so that such a laser can serve as an active OFCG. More than twenty years ago, the frequency comb of a mode-locked picosecond dye laser has first been used as an optical ruler to measure transition frequencies in sodium 4 2 . This route was further pursued in the seventies and eighties 4 3 ' 4 4 , but the attainable bandwidths were never sufficiently large to make it a widespread technique for optical frequency metrology. Broadband femtosecond Ti: sapphire lasers have existed since the

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i(f)

mi

J-u

Figure 1. Two consecutive pulses of the pulse train emitted by a mode locked laser and the corresponding spectrum (right). The pulse to pulse phase shift A

0.1 Hz. Thus, a frequency ratio measurement of these two optical signals can be carried out with smaller instabilites than that of an Yb/H-maser frequency ratio measurement, at least for short averaging times. This is demonstrated in Fig. 5. The dashed curve shows the Allan standard deviation SRAV of our H-maser. The data of the frequency measurements of the Iodine and the Ybstandard with respect to this H-maser are shown as triangles and squares, respectively. The SRAV of the Yb-laser qualitatively follows that of the H-maser, which limits the measurement for averaging times from 1 to 100 s. The SRAV of the Iodine -signal is larger than that of the H-maser for T>20 s. In fact, frequency comparisons of two such Iodine standards showed a SRAV of about 2xl0" 1 4 in this range and thus larger than of the H-maser. The SRAV of a frequency ratio measurement of two optical standards, on the other hand, is not limited by H-maser noise, as shown by circles in Fig. 5. The data depicted by solid circles have been derived from the Yb/Iodine beat signal as obtained from the last mixer in Fig. 2, whereas the open circles have been calculated from readings of the totalizing counters, as in Fig. 4.

141

-•-

-o-\ j-Yb/l 2 -n-- Yb/H-Maser

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1E-12-

- • - l2/H-Maser —

H-Maser

< 1E-13-

rr

CO

1E-140,01

100

Averaging Time x [s] Figure 5. Allan standard deviation of three frequency ratio measurements: Ybstandard/H-maser, Iodine-standard/H-maser and Yb-Aodine-standard. Note that the instability of the opticalfrequencyratio measurement is substantially smaller than that of the H-maser for averaging times below 10 s.

The i~m -dependence of the SRAV function of the ratio measurement indicates a white frequency noise level of Sv = 150 Hz2/Hz at 344 THz, which is again m good agreement with Fig. 3 and 4. 5. Conclusion In conclusion, we have demonstrated a novel concept for frequency measurement or synthesis concept which is capable of phase-coherently linking very different spectral regions in the optical and microwave spectral range without introducing additional noise. We have carried out frequency ratio measurements between optical frequencies with short-term instabilities superior to that of a microwave reference. Since the measurement uncertainties were clearly limited by the noise properties of the frequency standards, one may expect an even lower limitation due to noise contributions of the KLM laser, when better optical frequency standards become available. The transfer concept opens up new perspectives for future ultra-high precision applications, e. g. measurement of time variations of fundamental constants as soon as appropriate optical frequency standards are available.

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Acknowledgement We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft through SFB407 and contributions from Burghard Lipphard, Harald Schnatz, Christian Tamm. We are also indebted to Robert Windeler of Lucent Technologies for providing the microstructure fiber. References 1. Udem Th, Reichert J., Holzwarth R, and Hansch T. W., Accurate measurement of large optical frequency differences with a mode-locked laser, Opt. Lett. 24 (1999) pp. 881-883. 2. Udem Th, Diddams S. A., Vogel K. R., Oates C. W., Curtis E. A., Lee W. D., Itano W. M., Drullinger R. E., Berquist J. C , and Hollberg L., Absolute frequency measurement of the Hg+ and Ca optical clock transitions with a femtosecond laser, Phys. Rev. Lett. 86 (2001) pp. 4996-4999. 3. Stenger J., Tamm Chr., Haverkamp N., Weyers S, and Telle H. R., Absolute frequency measurement of the 435.5nm 171Yb+ clock transition with a Kerr-lens mode-locked femtosecond laser, Opt. Lett. 26 (2001) pp. 1589-1591 4. Niering M, Holzwarth R., Reichert J., Pokasov P., Udem Th., Weitz M., Hansch T. W., Lemonde P., Santarelli G., Abgrall M., Laurant P., Salomon C, and Clairon A., Measurement of the Hydrogen 1S-2S transition frequency by phase coherent comparison with a microwave Cesium fountain clock, Phys. Rev. Lett. 84 (2000) pp. 5496-5499. 5. Jones D. J., Diddams S. A., Ranka J. K., Stentz A., Windeler R. S., Hall J. L., and Cundiff S. T., Carrier envelope phase control of femtosecond mode-locked lasers and direct optical synthesis, Science 288 (2000) pp. 635-639. 6. Kramer G., Lipphardt B., and Weiss C. O., Coherent frequency synthesis in the infrared, Proc. 1992 Frequ. Contr. Symp. (1992), pp. 39-43, IEEE Cat. # 92CH3083-3. 7. Reichert J., Holzwarth R., Udem Th., and Hansch T. W., Measuring the frequency of light with mode-locked lasers, Opt. Comm. 172 (1999) pp. 59-63. 8. Telle H. R., Steinmeyer G., Dunlop A. E., Stenger J., Sutter D. H., and Keller U., Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement ands ultrashort pulse generation, Appl. Phys. B69 (1999) pp. 327-332. 9. Sutter D. H., Steinmeyer G., Gallmann L., Matuschek N., Morier-Genoud F., Keller U., Scheuer V., Angelow G., and Tschudi T.;Semiconductor saturableabsorber mirror-assisted Kerr-lens mode-locked Ti:Sapphire laser producing pulses in the two cycle regime, Opt. Lett. 24 (1999) pp. 631-233

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10. Ranka J. K., Windeler R. S., and Stentz A. J., Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm, Opt. Lett. 25 (2000) pp. 25-27. 11. Tamm Chr., Engelke D., and Buhner V., Spectroscopy of the electricquadrupole transition 2 S 1/2 (F=0) - 2D3/2 (F=2) in 171Yb+, Phys. Rev. A61 (2000) 053405. 12. Nevsky A. Y., Holzwarth R, Reichert J., Th. Udem Th., Hansch T. W., von Zanthier J., Walther H., Schnatz H., Riehle F., Pokasov P. V., Skvortsov M. N., and Bagayev S. N., Frequency comparison and absolute frequency measurement of I2-stabilized lasers at 532 nm, Opt. Comm. 192 (2001) pp. 263-272.

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FEMTOSECOND OPTICAL FREQUENCY COMB MEASUREMENTS OF LASERS STABILISED TO TRANSITIONS IN 88Sr+, 171Yb+, AND I2 AT NPL S. N. LEA, H. S. MARGOLIS, G. HUANG, W. R. C. ROWLEY, D. HENDERSON, G. P. BARWOOD, H. A. KLEIN, S. A. WEBSTER, P. BLYTHE, AND P. GILL National Physical Laboratory,

Queens Road, Teddington, Middlesex TW11 OLW, UK R. S. WINDELER

OFS, 700 Mountain Avenue, Murray Hill, New Jersey 070974, USA This paper reports absolute frequency measurements of trapped ion and HeNe/h systems using the NPL femtosecond comb. Two transition frequencies in laser-cooled single trapped ions have been measured: the 88Sr+ 5s 2Si/2 - 4d 2D;a electric quadrupole transition at 674 nm and the 171 Yb+ 4f146s 2Sm (F = 0) - 4f136s2 2Fm (F = 3) electric octupole transition at 467 nm. In addition, the frequency of the helium-neon laser NPL-S stabilised to four hyperfine components of the 127i2 11-5 R(127) line at 633 nm has been measured.

1

The NPL femtosecond optical frequency comb

Femtosecond laser frequency comb generators [1] are currently revolutionising absolute optical frequency metrology, leading to measurements of optical frequency standards relative to the microwave primary standard with uncertainties limited at the part in 1014 level by the uncertainty of the optical standards themselves [2]. In this paper we report the results of preliminary measurements of three optical frequencies, two of which are based on transitions in cold, trapped single ions: the strontium ion standard at 674 nm [3,4] and the ultra-narrow octupole transition at 467 nm in ytterbium [5,6]. The third is the iodine-stabilised HeNe laser at 633 nm, which, at NPL, is the realisation of the primary standard for length metrology [4]. The measurements reported below were made using an octave-span frequency comb based on a Kerr-effect mode-locked Ti:sapphire laser with spectral broadening in microstructure fibre (fig. 1). The laser is constructed from a kit supplied by KMLabs [7] and is pumped with 4.5 W of single frequency light at 532 nm. The laser is a linear cavity design with dispersion compensation by means of intracavity prisms. The cavity length is set to produce a pulse repetition rate/ R near 88 MHz; fine control of/R is provided by a cavity fold mirror mounted on a piezo element. The intermode beat spectrum is detected using an avalanche photo-diode (APD). The intermode beat at the 10th harmonic of/R is used to stabilise and count / R . In the first stage, the beat at 10 x/ R is mixed with the output of an rf synthesiser at a frequency/ s to generate a signal at 9.8 MHz. This signal is used for two purposes. Mixed with a reference 9.8 MHz signal in an analogue phase comparator, it

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produces a dc error signal which is fed back to the laser via the piezo-mounted fold mirror. Mixed with a reference 10 MHz signal, it is used to digitally phase-lock (at 200 kHz) a 200 MHz VCO using a division ratio of 1000. The VCO output is counted using an HP53132A frequency counter. The counted frequency fc and the synthesiser frequency/s are used to determine the repetition rate/ R : f

mode-locked Tftsapphire laser

S

R

= _ /s-10MHz + /c 1000 10

cavity end mirror (plezo tilt contra!)

dispersion compensation^

piezo-mounted fold mirror

output coupler microstructure fibre

dlchrolc beamsplitters

—%> %— >950nm keOOnrn

SHGII inKTP

^

$

optica! frequency standard /be

^/CE

variable delay tine

Figure i . Schematic diagram of the femtosecond optical frequency comb set-up.

The output of the femtosecond laser is spectrally broadened in a 23 cm length of microstrocture fibre fabricated by Lucent Technologies [8]. The carrier envelope offset frequency/ceo is determined from the beats spectrum of light in a bandwidth of a few nm around 1.06 pin, frequency doubled in KTP, with light in the equivalent bandwidth around 530 nm. The beat frequency fi^ of the laser being measured with the nearest comb mode m is also determined. Both these beats are detected using APDs; the signal-to-noise in these beats rather low, around 15 - 20 dB in 1 MHz bandwidth. Analogue tracking oscillators (TOs) are used to filter and amplify these beats to provide countable signals in the range 25 - 35 MHz. The tilt of the laser cavity end mirror in the plane of the laser cavity can be adjusted via a piezo-electric stack. The carrier envelope offset is not servoed but this piezo control and the synthesiser frequency / s are adjusted to sttfcw and/ teat within the range of the TOs. The measured frequency J j ^ is determined from/R, fcm / t o t and the mode number: /meas

m

J R — J ceo — /beat "*" fc

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For the Sr+ and Yb+ measurements, /0ffset is the offset of the trapped ion transition frequency from the frequency of a very low drift ULE cavity to which the probe laser is stabilised (the light beating with the fs comb to yield /beat is at the frequency of the ULE cavity-stabilised laser). For the HeNe/I2 measurement,/0ffset is a fixed 40 MHz offset between the I2-stabilised laser NPL-S and a transfer HeNe laser. The mode number m and the signs of the beats / ceo and f^ are determined on the assumption that the measured frequency is known a priori to better than a few MHz. The frequencies/c, /ceo> and f^n a f e counted by HP53132A frequency counters which are synchronously gated and read via GPIB by PC-based software. (fc is generated by two nominally identical digitally-phase locked VCOs which are counted on separate counters.) For most of the data runs contributing to the measurements described below, a gate time of 1 s was used although a gate time of 3 s was occasionally tried with no significant difference in the measured frequency. Between successive runs the sign of the beat / ceo or f^^ was changed; the consistency of the measured frequency from run to run is thus an indication that the TOs introduce no significant offset. The synthesiser frequency/s was also adjusted between most runs, to compensate for a long-term mechanical drift of the femtosecond laser cavity length, and manually recorded. All the rf synthesisers and frequency counters are referenced to the 10 MHz output of a hydrogen maser forming part of the clock ensemble generating the timescale NPL(UTC). Analysis of data for this maser shows that over the period of the measurements discussed below, the maser reference provided traceability to the SI second at the level. The 10 MHz signal is transmitted to the fs laser laboratory via 250 m of RG213 coaxial cable. The round trip delay time measured using the 1 pulse per second output of the maser showed a relative diurnal sinusoidal variation of 2 x 10"4 superimposed on a longer-term drift. Both these effects are strongly correlated to external temperature. The maximum rate of change of the delay can be interpreted as a frequency pulling at the 1 x 10"13 level; however most of the data runs were taken in the early evening when the cable delay was near a turning point. The uncertainty in the 10 MHz reference frequency is not therefore a significant contribution to the overall uncertainty of the measurements reported here.

2

Measurement of the 88Sr+ 2 S W - 2D5/2 transition in a single trapped ion

An optical frequency standard based on the 5s 2 S 1/2 - 4d 2D5/2 electric quadrupole transition in a single, trapped strontium-88 ion has been developed at NPL [3] and NRC [9]. This was the first trapped ion standard to be adopted as a recommended radiation for the realisation of the metre [4]. For details of the NPL set-up, see [3]. Femtosecond comb measurements of the strontium trapped ion standard were made on two days. The 674 nm probe laser is locked to a high-stability ULE cavity with a drift rate of typically less than 1 Hz/s. Light from this laser is sent to the fs

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laser lab via a single-mode fibre link. The probe laser light is frequency shifted by an amount/0ffset in a double-pass acousto-optic modulator (AOM) before being sent to the ion trap. The frequency of this shifted light is locked to the centre of the Zeeman structure of the 2Sm - 2D5/2 transition by a four-point servo scheme using the two Am = 0 Zeeman components. The transition frequency is determined by summing the mean value of the ULE cavity frequency as measured by the fs comb and the mean value of/offset over the same time interval. Figure 2 plots fs comb measurements made synchronously with the ion trap offset frequency in lock. On 23rd August 2001, the ion trap offset was re-locked between most fs comb measurements. On 29th August, all but the final four measurements were made during a single period of 90 minutes during which the ion trap offset remained locked. The final three results may have been affected by a problem with the 674 nm laser servo. Each fs comb measurement contains typically 300 one second measurements, the error bar shown on each point is the standard error of the mean of this data set. From these two days' data, we determine the transition frequency to be / Sr+ = 444 779 044 095.6 (0.3) kHz (1 ± 7 x 10"u). The distribution of individual femtosecond laser measurements is non-normal; the quoted standard uncertainty assumes a rectangular distribution. Systematic errors from the ion trap are insignificant at this level: an intercomparison of three similar traps showed offsets below 50 Hz [3]. 96.6 96.4 N

5 96.2 o O

96.0

° hr^

95.8

1

95.6 95.4

•H

6uWlV>

95.0

Figure 2. Measurements of the 88Sr+ 2Sm - 2D5/i transition. • 23rd August, • 29th August 2001. Each point represents a single fs laser measurement. The solid line represents the mean frequency and the dotted lines represent the assigned uncertainty (see text).

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This measurement is in good agreement with the result obtained by the NRC group using a phase-coherent frequency chain [9] and consistent with a previous interferometric measurement at NPL [10]. Measurement of the m Yb+ 2S

1/2 — F7/2 transition in a single ion The 4f146s 2S 1/2 ( F = 0) 4f136s2 2F7/2 (F = 3) octupole transition at 467 run in 171Yb+ has a natural linewidth of the order of a nanosecond. The observed linewidth of the transition, currently about 4.5 kHz, is entirely due to the linewidth of the interrogating laser. Experimental details of the ytterbium ion trap set-up are given in [6], together with a discussion of some of the systematic effects which may limit the performance of a frequency standard based on this transition.

X

0.780

5 to ?

H ;-+

0.778

ggj^jjgjgg 0

2000

4000

6000

8000 10000 time/seconds

12000

14000

16000

18000

Figure 3. Measurements of the 171Yb+ 2S\a - 2Fm transition. Each point represents a single fs laser measurement, plotted as a function of the mid-point time of the run. The solid line represents the mean frequency (before correction for AC stark and 2nd order Zeeman shifts); the dotted lines represent the standard deviation, and the dashed lines the standard error of the mean, of the set of measurements.

Measurements of the ytterbium octupole transition frequency were made on a single day (5th September 2001). The measurement scheme is similar to that for strontium except that the probe light is obtained by frequency doubling a Ti:sapphire laser at 934 nm; it is this laser which is stabilised to the ULE cavity. Moreover, the probe light is not locked to the reference transition via the AOM but is simply stepped in frequency through the resonance to build up a quantum jump profile from which the mean offset of the resonance from the ULE cavity frequency is determined. Measurements of the ion trap offset and the ULE cavity frequency are not

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synchronous; the mean value quoted below is obtained by determining the ULE cavity drift from the ion trap scans and hence obtaining an appropriate value of/offset for each fs measurement. The value obtained from this one day of measurement is 642 121 496 776.4 (0.4) kHz where the l o uncertainty quoted is the standard error of the mean of the fs comb measurements (fig. 2). Two corrections are applied to this frequency for systematic effects in the ion trap: AC Stark shift (-4.0 (1.2) kHz) and 2nd order Zeeman shift (+0.17 (3) kHz) [6], giving a final value of / Yb+ = 642 121 496 772.6 (1.3) kHz (1 ± 2 x 10 12 ). This result is consistent with previous interferometric measurements at NPL, the most recent of which, made with the same ion trap set-up and measurement methodology as the fs comb measurement, yielded /Yb+ = 642 121 496.54 (0.17) MHz. An earlier measurement, for which the probe laser was stabilised in the blue to a Te2 absorption, yielded / Yb+ = 642 121 498.1 (0.8) MHz [5]. 4

Measurements of HeNe/I2 laser NPL-S 22

ffl'4g:

ft+*7

Figure 4. Measurements of the HeNe/I2 laser NPL-S, • 8th August, D 13th August, • 17th August, O 28th August 2001. Each point represents a single fs laser measurement. The solid line represents the mean frequency; the dotted lines represent the standard deviation, and the dashed lines the standard error of the mean, of the set of measurements.

Measurements have been made of the laser system NPL-S stabilised to components d, e, f, and g of the 11-5 R(127) line in 127I2. The results are summarised in fig. 4.

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The individual fs laser measurements are plotted relative to the CIPM recommended frequency for each component [4], after applying corrections for iodine cell cold finger temperature and laser power. The mean, expressed as a difference from the CIPM recommended values, is NPL-S = CIPM + 15.58 (0.22) kHz (1 ± 5 x 10"13) where the quoted l a uncertainty is the standard error of the mean of all the measurements. In an intercomparison at BIPM in 1995 the laser NPL-S was measured relative to the laser BIPM-4, giving the result [11]: NPL-S = BIPM-4 + 7.4 (2.5) kHz. Assuming that laser NPL-S has not changed its frequency since this measurement, we can infer that the frequency of the laser BIPM-4 is 8.2 (2.5) kHz greater than the CIPM value, in good agreement with the 7.8 (1.2) kHz offset obtained from fs comb and phase-coherent frequency chain measurements at JDLA and NRC [12]. 5

Summary

We have implemented a self-referenced femtosecond laser optical frequency comb which has been used to make preliminary absolute frequency measurements with parts in 1013 precision. The measurement of the 88Sr+ 674 nm 2Si/2 - 2D5/2 transition is in good agreement with a measurement at NRC using a conventional phasecoherent optical frequency chain [9]. Both this measurement and the measurement of the 171Yb+ 467 nm 2Si/2 - 2F7/2 transition are consistent with previous interferometric measurements at NPL. The measurement of the 633 nm HeNe/I2 standard supports the conclusion of the JILA/NRC/BIPM measurements [12] that the CIPM recommended values are around 8 kHz too low. Further work is in progress to improve the performance of our system and to verify its accuracy. In particular, measurement of our methane-stabilised HeNe laser system at 3.39 (irn will provide a test of the accuracy of the fs comb at the 3 x 10"13 level as its frequency is known to this accuracy from intercomparisons with rf-toinfrared harmonic frequency chains over a three-year period [13]. This experiment can be performed either by measuring the fourth harmonic of the methane frequency at 848 nm or by measuring it as a frequency difference between 674 nm and 841 nm [14]. In the latter case, the measurement will be independent of fceo. Further measurements of the Sr+, Yb+, and HeNe/I2 frequencies are planned, together with measurements of other working standards including the DL/Rb 2-photon standard at 778 nm [15] and the Nd:YAG/I2 standard at 532 nm [16].

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Acknowledgements

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Thanks are due to P.B. Whibberley and J. Clarke for their assistance with the cable delay measurements and H-maser data and to N. Moore for technical assistance. This work is supported by the UK National Measurement System Length Programme under contract LE99/A01. References 1.

2. 3.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16.

Udem T. et al, Phys. Rev. Lett. 82 (1999) 3568-71; Jones D. et al, Science 288 (2000) 635-9; Holzwarth R. et al, Phys. Rev. Lett. 85 (2000) 2264-7. Udem T. et al, Phys. Rev. Lett. 86 (2001) 4996-9; Stenger J. et al, Opt. Lett. 26(2001)1589-91. Barwood G.P., Gao K., Gill P., Huang G. and Klein H.A., IEEE Trans, lustrum. Meas. 50 (2001) 543-7; SPIE Proc. 4269 (2001) 134-142; these proceedings. Quinn T.J., Metrologia 36 (1999) 211-244. Roberts M., Taylor P., Barwood G.P., Rowley W.R.C. and Gill P., Phys. Rev. A 62, (2000) 020501R. Webster S.A., Barwood G.P., Blythe P. and Gill P., these proceedings. Kapteyn-Murnane Laboratories, 3509 Kirkwood PL, Boulder, CO 80304, USA. Ranka J.K., Windeler R.S. and Stentz A.J., Opt. Lett. 25 (2000) 25-27. Bernard J.E., Madej A.A., Marmet L., Whitford B.G., Siemsen K.J. and Cundy S., Phys. Rev. Lett. 82 (1999) 3228-31. Barwood G.P., Gill P., Klein H.A. and Rowley W.R.C, IEEE Trans, lustrum. Meas. 46(1997) 133-136. Darnedde H. et al, Metrologia 36 (1999) 199-206. Ye J. et al, Phys. Rev. Lett. 85 (2000) 3797-3800. Gubin M. et al., these proceedings. Lea S.N., Macfarlane G.M., Huang G. and Gill P., IEEE Trans. lustrum. Meas. 48 (1999) 578-582; Margolis H.S., Lea S.N., Huang G. and Gill P., Proceedings of the 14th EFTF (2001) 194-198. Edwards C.S., Barwood G.P., Gill P. and Rowley W.R.C, these proceedings. Macfarlane G.M., Barwood G.P., Rowley W.R.C. and Gill P., IEEE Trans. Instrum. Meas. 48 (1999) 600-603.

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Part VI

CPT Standards

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COHERENT POPULATION TRAPPING AND INTENSITY OPTICAL PUMPING: ON THEIR USE IN ATOMIC FREQUENCY STANDARDS JACQUES VANIER12, MARTIN LEVINE1, DANIEL JANSSEN1 AND MICHAEL DELANEY1 2)

1} Kernco Inc., Danvers, MA, USA. Departement de Physique, Universite de Montreal, Montreal, Canada.

The paper summarizes the relative advantages and disadvantages of Coherent Population Trapping (CPT) and Intensity Optical Pumping (IOP) for the implementation of a passive atomic frequency standard. The paper outlines the basic principles common to both CPT and IOP when using laser optical pumping, and makes explicit their similarities and their differences. The paper describes recent experimental results obtained in the same cell on the characteristics of the CPT and IOP8 Rb-hyperfme resonance line. 1. Introduction

The advent of the solid state laser has opened new avenues in the field of optically pumped frequency standards. Such lasers have spectral widths of the order of 100 MHz or less and have a wavelength appropriate to optically pump alkali atoms such as cesium and rubidium. In a first approach they are used directly to replace the spectral lamp in the case of the passive rubidium standard [1]. Laser diodes can also be used to optically pump cesium for which no isotopic filtering is possible [2, 3]. The ground state hyperfine resonance line is observed as usual by means of the double resonance technique requiring both optical and microwave excitation in a resonant cavity. It is noted that in that approach, the laser acts as a spectral lamp with a high spectral purity. For this reason this type of pumping is called Intensity Optical Pumping, henceforth abbreviated IOP. In a second approach, such lasers are used to generate two coherent radiation fields coupling both ground state hyperfine levels of an alkali atom such as cesium or rubidium to one of the P states. Interference takes place in the excitation process and at exact resonance no optical absorption takes place. A resonance line characteristic of the ground state hyperfine transition is observed either in the fluorescence or in the transmitted light. No microwave excitation is required. In this technique the atoms are all trapped in the ground state and for this reason the phenomenon has been called Coherent Population Trapping, henceforth abbreviated CPT [4].

The object of the present paper is to compare the basic characteristics of IOP and CPT in connection to their use in the implementation of a laser-opticallypumped atomic frequency standard. The discussion is limited to the basic physical

155

156 phenomena involved. It will be shown that CPT offers greater promises than IOP, regarding frequency stability and size.

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2. Basic physical principles of IOP and CPT The following discussion is limited to the case of the alkali atom 87Rb. However, most of the conclusions reached can be transposed to the case of other alkali atoms such as 133Cs. 2.1 Optical pumping in IOP and CPT In the present discussion, we use a three-level model illustrated in Fig. 1. In the case of IOP only one radiation field, normally at co2, is applied to the ensemble and the hyperfine resonance line is detected by applying microwave power at the hyperfine frequency. In CPT the ensemble is exposed to two radiation fields at co, and (02 and no microwave power is applied.

Figure 1. Three-energy level model used to illustrate the technique of IOP and CPT. The unperturbed hyperfine frequency is vu = 6 834.682 612 8 MHz. In IOP, only one radiation field, at 0)2, is present and microwave energy is applied to the atoms at the hyperfine frequency. In CPT no microwave energy is applied at vM. This three-level model is adequate to explain the data observed and is used

throughout our analysis for either the IOP or CPT approach [5, 6]. In practice, the transition of interest for frequency standard application is that between the levels F=l, mF = 0 and F=2, mF = 0 of the ground state. Yi ar>d Y2 a r e the relaxation rates of the ground state population and coherence respectively. T* is the decay rate of atoms in the excited state, including the effect of spontaneous emission and collisions with the buffer gas atoms.

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The experimental setup used to observe the hyperfine resonance line by means of either IOP or CPT in the same cell is illustrated in Fig. 2. Either the transition to P.„ (X=794 nm) or to P „ (h=7&0 nm) can be used. Resonance cell:

Cavity

Photodetector

To recorder

Figure 2. Experimental arrangement used to observe "Rb hyperfine resonance by means of both CPT and IOP techniques. In the case of IOP, the microwave generator is used to apply energy to the cavity and excite transitions in the ensemble at the hyperfine frequency. In the case of CPT, no cavity is present and the microwave generator is used to modulate the laser frequency through the current source at a subharmonic of the hyperfine frequency. 2.1.1 Intensity Optical Pumping

technique

In the case of IOP the atoms accumulate in level F=2 upon optical pumping and the resonance cell becomes transparent since the number of absorbing atoms in level F=l is depleted. If microwave energy at the hyperfine frequency is applied to the cavity, transitions are excited between the two ground state hyperfine levels and the level F=l is repopulated. Light absorption is re-established and is detected at the photodetector. The resonance signal observed has all the characteristics of the ground state hyperfine transition: a large atomic line Q and a relative independence of environmental parameters. In a practical frequency standard synchronous detection techniques are used to lock the frequency of the microwave generator to the hyperfine resonance.

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2.1.2 Coherent Population Trapping technique In this case, optical pumping is done by means of two laser radiation fields at C0i and CO2 in a so-called A scheme, as illustrated in Fig. 1. When the two radiation fields angular frequency difference (co2 - d)^ is equal to the ground state hyperfine angular frequency, 2rtVM, an interference effect appears in the excitation process and no absorption takes place. All the atoms are trapped in the ground state levels. The system is said to be in a dark state and the phenomenon is observed either on the emitted fluorescence as a so-called "dark line" or on the transmitted radiation as a "bright line". This resonance line has many of the same characteristics as those of the hyperfine resonance observed in the case of IOP described above. In the experimental setup used, the laser is frequency modulated at one half the hyperfine frequency. In that case, the two first sidebands generated are separated by a frequency equal to the hyperfine frequency and are used as the radiation fields producing the CPT phenomenon as illustrated in Fig. 1 [7, 8]. No microwave cavity is required since there is no direct excitation of the atomic ensemble at the hyperfine frequency. In principle either the transmission or the fluorescence signals could be used for implementing a frequency standard. However, the fluorescence signal causes incoherent optical pumping at high alkali atom densities, which reduces the ensemble coherence and strength of the signal. When the transmission signal is used, nitrogen is used as buffer gas to quench the fluorescence. 3. Basis of comparison In the implementation of an atomic frequency standard, several goals may be selected depending on the desired application. In general, accuracy and frequency stability are basic characteristics aimed at. In present standards, the interest is limited to frequency stability since the buffer gas required causes a frequency shift that is not always reproducible in manufacturing cells. Another goal, important for field applications, is the realization of a standard with a small volume. This comparison of the IOP and CPT approaches will thus be limited to these two characteristics. The frequency stability of a passive frequency standard of the type discussed here is given by [5]:

(S/N)1'^1'2

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where K is a parameter that depends on the type of modulation used in the servo loop and is of the order of 0.2. The term S/N is the signal to noise ratio, T is the averaging time and Q, is the atomic line Q defined as Q1 = vM/Av1/2

(2)

where AVi/2 is the line width at half the height. The hyperfine resonance line is broadened by several relaxation mechanisms common to both approaches, CPT and IOP. They are: a) Residual collisions with the walls, which destroy the coherence in the system, and escape from the region of interaction with the laser beam. These two relaxation mechanisms have the same effect. The associated relaxation rate is called yw b) Collisions of the Rb atoms with the buffer gas atoms, which cause also a loss of coherence. The rate is called ybg. c) Spin-exchange collisions between Rb atoms with a rate YseThese relaxation rates add linearly. There are also other broadening mechanisms that are specific to the particular technique used. Case of IOP: In this case two other broadening mechanisms must be considered. They are the optical pumping interaction that acts as a relaxation process and the microwave radiation applied to excite transitions between the hyperfine levels that causes saturation. Calculation shows that the total line width is [5]: Av1/2 = (l/ 7I )( Yw+ Y bg ne+GC/2r , )(S+l) 1 ' 2

(3)

where S is the saturation parameter defined as:

s = ^hX

(4)

In this equation c o ^ is the Rabi angular frequency associated with the microwave excitation, and Yi' a n d Y2' include all relaxation and broadening mechanisms mentioned above. The term o\op2/2r* is the the broadening caused by the optical excitation. It is convenient to define the optical pumping rate r p as:

i>avop2/r* where co^is the optical Rabi angular frequency.

(5)

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Case of CPT: In this case, there is no microwave power applied and only the laser radiation needs to be taken into account. The added broadening is equal to co^V T* and the line width is given by [6]: Av w = (l/«)(Y.+Ylf+Y-+0W1f)

(6)

From this analysis it is clear that CPT has an advantage over IOP because of the absence of microwave power broadening in the first case. In the limit where an ideal laser is used as pumping source, the noise is proportional to the background light intensity reaching the detector, in that case, S/N is proportional to the contrast a defined as a - 8Ml V^

(7)

where V^ and SM are the background and hyperfine signal amplitudes as measured at the output of the V/I converter shown in Fig. 1. The. contrast is of the order of 1to10 % depending on experimental conditions. 4. Experimental results Representative hyperfine resonance signals are shown in Fig. 3. In all measurements

Tftrf

MPS * M t M

IOP

4

^ 3

S£$T

,»*0»»i

CPT

Figure 3. Typical IOP and CPT hyperfine resonance traasmission signals observed at 75 "C in a ceil containing Rb" and a buffer gas mixture.

related to the IOP configuration, the cavity shown in Fig. 2 was replaced by a simple loop radiator placed in the proximity of the resonance cell. The atomic ensemble was thus exposed to a travelling wave. However, since all experiments were done with a cell containing a buffer gas at relatively high pressure, line narrowing through Dicke effect took place and there was no Doppler broadening present [9]. This

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arrangement allowed measurements to be made using either the IOP or the CPT technique in the same cell with the same laser-pumping source without altering the optical section of the system. 4.1 Line vndth and contrast Measurements of line width and contrast were made using both CPT and IOP approaches. A typical result for the contrast and line width obtained with the CPT technique is shown in Fig. 4. It is observed that the signal reaches a contrast larger than 5 % with a resulting line width of 500 Hz at a V„ of about 3 volts. Measurements of this nature have been made over a temperature range from 65 to 85 °C.

2

4

6

8

Laser infensty at detector [V] Figure 4. Contrast and line width of the "Rb hyperfme resonance line as observed in a cell at a temperature of 75 *C as a function of laser intensity using the CPT technique.

The comparison with IOP signals cannot be done directly since in the case of IOP the contrast and line width are functions of two parameters, light intensity and microwave power. However, a somewhat quantitative comparison can be made by setting the microwave power at fixed values. Such results are shown in Table 1. The laser intensity was such as to develop a voltage Vdof 2 volts at the detector. The

162

small difference between the value of a^ reported here for CPT and that of Fig. 4 is due to a difference in modulation index in the two measurements.

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p

IOP II

CPT

[mV]

s h /v bg

Av1/2 [Hz]

q

[v] lOdBm

1.60

34.5

1.73 %

1175

0.15

-2dBm

1.60

6.7

0.34 %

380

0.089

N/A

1.45

72.8

3.64 %

381

0.95

IO"4

Table 1. Comparison of contrast and line width at a temperature of 75 °C obtained in the IOP and CPT techniques.

As seen in Table 1 it appears that the CPT approach is superior to IOP relative to all parameters. Although in the case of IOP the signal contrast can be increased considerably by increasing the microwave radiation field applied to the cell, the consequence is an important resonance line broadening reducing the line Q and the quality figure. 4.2 Light shift A phenomenon that may affect frequency stability is the light shift that originates from an interaction of the laser radiation with the atoms [10]. It is essentially an ac Stark effect affecting the position of the atom energy levels. We define A0 as the detuning of the laser relative to the frequency of the transition as illustrated in Fig. 5.

F=2

Figure 5. Definition of Ao, the laser detuning from the optical transition.

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When only one radiation field is present, as in the case of IOP, the light shift is given by [8]: A(oLS =-(1/4)

2

(r*/2) +A^

..2 FRop

(8)

Measurements have been reported in 87Rb on the size of this effect in a typical situation using laser optical pumping [1], It was found that the results agreed with the shape of the function given in Eq. 8. For the case where A02 « (r*/2)2, the shift is linear with laser detuning with a sensitivity of the order of 1.1 x 1Q40 per MHz of detuning and a laser power density of 250 JAW. The behavior of the resonance frequency as a function of the microwave power used to modulate the laser is shown in Fig. 6 for the case of CFr in a 87Rb cell. CPT RF POWER RESPONSE; COMBINED DATA

Figure 6. Light shift observed in CPT m "Rb for a laser tuned to the optical resonancefrequencyas a function of the laser modulation microwave power at 3.4 GHz .

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In this case, since the optical pumping is done from both ground state levels there is no first order light shift as in the case of IOP. However, all the sidebands interact with the levels with which they are not resonant and produce an off resonance light shift. Its total value is obtained through a summation of Eq. 8 over all sidebands and energy levels. In the three-level model, it is found that the light shift consists of two components one independent of the frequency of the laser and one with a quadratic dependence on the laser frequency [11]. This last component is very small and, in view of its quadratic dependence on laser tuning, can be neglected. The other component, called the power light shift, can be reduced by setting the index of modulation to an appropriate value [11, 12]. 4.3 Short term frequency stability The short-term frequency stability expected from a setup operated either in the IOP or CPT mode may be calculated from Eq. (1). We assume that the pumping laser is ideal and monochromatic. We assume also that the light intensity reaching the detector is large and that the resulting noise is entirely due to shot noise. We set the modulation depth in the frequency-lock-loop to one half the value of the line width [5]. Using the data of Table 1, the signal to noise ratio is readily calculated as: IOP (P^w= -2dBm)

(S/N)"2 = 1.6x 104

CPT

(S/N)M = 1 . 6 x 1 0 '

The expected short term frequency stability is: a(T) = 7 x 10'13 T"1/2 IOP 1/2 o(T) = 7 x 10-'V CPT If more microwave power is used in the case of IOP, a larger contrast is achieved and a better signal to noise ratio is obtained. However, the line width increases proportionally and the expected frequency stability remains lower than in the case of CPT. This analysis shows the theoretical superiority of CPT regarding frequency stability. Measurements, using an open optical bench arrangement gave a frequency stability of the order of 6 x 10'12 for an averaging time of 1000 s. Both systems behave similarly over the range 100< T< 2000s The frequency stability obtained is very encouraging in view of the nature of the experimental arrangement used in these measurements. The calculations made above were based on the use of ideal monochromatic lasers, without noise. The reality is far from this assumption. Solid state lasers are not monochromatic,

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have spectral widths of the order of 50 to 100 MHz, and are generally characterized by amplitude and frequency fluctuations. This characteristics is common to either edge emitting laser diodes or vertical cavity surface emitting lasers (VCSEL). These fluctuations appear as noise at the detection and may affect frequency stability either directly or by conversion through the residual light shift [13, 14, 15, 16]. Furthermore in the open experimental setup used, there were many other sources of noise present such as air motion affecting the light beam, temperature fluctuations of the laser and optical components, and mechanical vibrations. No special care was taken in the present setup to minimize these sources of noise. It is expected that in the case of CPT in a compact system, in which all components are rigidly assembled and modulation levels are optimized for minimum light shift levels, a frequency stability closer to the calculated value will result. 4.4 Physical dimensions The size of a frequency standard based on the IOP approach is largely determined by the structure necessary to sustain the microwave field at the site of the atoms. Although many approaches have been suggested to face this restriction, the problem remains fundamental. In CPT no microwave cavity is required. 5. Conclusion The following important conclusions can be drawn from the results reported above: 1) Regarding signal size, contrast, and frequency stability the CPT approach appears to be superior to the IOP approach. 2) The light shift in the CPT approach can be made smaller than in the IOP approach using a laser as optical pumping source. This is done by adjusting the laser index of modulation to an appropriate value. 3) In connection to physical dimension, CPT offers considerable advantage over IOP due to the absence of the microwave cavity, making possible the use of smaller solenoid and magnetic shields. 4) The problem of the laser availability is the same for both approaches. References [1] [2]

Lewis L. L. and Feldman M., Proc. 35th Ann. Symp. on Frequency Control (Washington DC: Electronic Industries Association) (1981), 612. Chantry P.J., Liberman I., Verbanets W.R., Petronio C.F., Cather R.L. and Partlow W.D. Proc. IEEE Int. Symp. on Frequency Control, (1997).

[3]

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[4] [5] [6] [7] [8] [9] [10]

[11]

[12] [13] [14] [15] [16]

Rovera G., De Marchi A. and Vanier J., IEEE Trans. Instrum. Meas. IM25, (1976), 203. Alzetta G., Gozzini A., Moi L. and Orriols G., Nuovo Cimento B 36 (1976), 5. Vanier J. and Audoin C , "The Quantum Physics of Atomic Frequency Standards", Adam Hilger, Bristol, U.K., (1989). Vanier J., Godone A. and Levi F., Phys. Rev. A58, (1998), 2345. Cyr N., Tetu M. and Breton M., IEEE Trans. Instrum. Meas. 42, (1993), 640. Levi F., Godone A., Novero C. and Vanier J., Proc. of the Eur. Forum on Time and Frequency, Neuchatel, Switzerland, (1997). Dicke R. H., Phys. Rev.Lett. 18, (1953), 472. Cohen-Tannoudji C. Thesis, Faculte des Sciences de l'Universite de Paris, 1962, unpublished; Barrat J.P. and Cohen-Tannoudji C. , J. Phys. Radium 22, (1961), 329. Vanier J., Godone A. and Levi F., Joint Meeting of the 13th European Frequency and Time Forum and IEEE International Frequency Control Symposium, Besancon, France, April 1999; Levi F., Godone A., and Vanier J., IEEE Trans. Ultrasonics, Ferroelectrics, and Freq. Control, 47, (2000), 466. Zhu M. and Cutler L., Precise Time and Time Interval (PTTI) Systems and Applications Meeting, Reston, Virginia, USA (2000). Mileti G., Doctoral thesis, Universite de Neuchatel, Neuchatel, Suisse, (1995). Levi F., Doctoral thesis, Politecnico di Torino, Torino, (1995); Mileti G., Deng J., Walls F. L., Jennings D. A. and Drullinger R. E., J. Quant. Electr. 34, (1998), 233. Kitching J., Knappe S., Vukiecevic L., Hollberg L., Wynands R. and Weidmann W., IEEE Trans. Instrum. Meas. IM 49, (2000), 1313.

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COMPACT MICROWAVE FREQUENCY REFERENCE BASED ON COHERENT POPULATION TRAPPING1^

JOHN E. KITCHING*, HUGH G. ROBINSON AND LEO. W. HOLLBERG Time and Frequency Division, The National Institute of Standards and Technology, M.S. 847.10, 325 Broadway, Boulder, CO 80305-3328 E-mail: [email protected] SVENJA KNAPPE AND ROBERT WYNANDS Institut fur Angewandte Physik, Universitdt Bonn, D-53115, Bonn, Germany A simple, compact and low-power microwave frequency reference based on CPT resonances in Cs vapor is described. The 14 cm3 physics package exhibits a resonance width of 620 Hz at 4.6 GHz, a short-term fractional frequency instability of \.3xl0~'° l^rl(,s), and dissipates less than 30 mW, not including temperature control. We discuss the prospects for extreme miniaturization to sub-millimeter dimensions.

1

Introduction

Atomic frequency references and quartz-crystal oscillators are, in some sense, complimentary technologies. Atomic frequency references have good accuracy and long-term stability but are large, complex and expensive to build. Quartz-crystal oscillators, on the other hand, have poor accuracy but superb short-term stablity, and are small, simple and inexpensive. A significant gap exists, both in performance and design, between the two types of frequency reference, as shown in Table 1. There are two obvious appoaches to bridging this gap: to make quartz crystals better (and probably larger and more expensive) or to make atomic clocks cheaper and simpler (and probably less accurate). Table 1. Comparison of frequency references.

Atomic Reference Quartz-crystal oscillator

Accuracy lo" 10 10"7

rjy(l s) Size ^xTcr'T loo'cni 3 "" 10"'2 10 cm 3

Power 10"w " 1W

Cost $2,000 $100

Applications for compact atomic clocks (or high-performance quartz crystals) are numerous, ranging from the military [1] to advanced telecommunications [2] and instrumentation. Military applications include fast-acquisition GPS receivers, anti-jam communications systems, and advanced identification and surveillance technology. These tend to require more compact devices of lower power. Commercial applications, such as telecommunications network synchronization and laboratory instrumentation, mostly require devices of lower cost. We describe here our efforts to design and build compact atomic clocks for these kinds of

167

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applications. We have focused on using coherent population trapping (CPT) rather than a conventional optical-microwave double-resonance design due to the simplicity and increased potential for extreme miniaturization and low-power operation. 2

The CPT-CIock

Research on coherent population trapping [3,4] is increasing for use in a variety of applications from atomic clocks [5,6] to magnetometers [7], although no

Detector

D-EE>t>

852 nm

Modulated

_,

„

F=3 (a)

(b)

Figure 1. An atomic clock based on CPT.

commercial systems have yet been brought to market. In a CPT clock, the atomic microwave resonance is probed using only optical fields, separated in frequency by the atomic ground state hyperfine transition splitting and tuned to be simultaneously in resonance with an optical transition. The fields are passed through a thermal vapor of atoms and the DC absorption is monitored as a function of the difference frequency between the fields. When this difference frequency exactly equals the atomic hyperfine splitting, a change in the absorption occurs: atoms are optically pumped into a coherent superposition of the ground states for which quantum interference prevents the absorption of light [8]. In our system [9], the current of a semiconductor laser is modulated at the first sub-harmonic of the hyperfine frequency such that the two first-order sidebands are resonant with the atomic levels, as shown in Figure 1. The frequency of the modulation signal, which is derived from a crystal oscillator and synthesizer, is then locked to the atomic absorption line using the transmitted power through the cell. It is interesting and important that, with this method, no microwave fields are applied to, or detected from, the atoms. Both the atomic excitation and the state detection are done with only optical fields. Although not used in our implementation of the CPT-clock, the CPT superposition state has a magnetic moment oscillating at the

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hyperfine splitting frequency, which can also be detected [10] (with a microwave cavity, for example) to determine whether the microwave frequency is on resonance. 3

Clock Design

Several aspects of the clock design are important for miniaturization and low-power operation. The first of these is the choice of laser: we use here a vertical-cavity surface-emitting laser (VCSEL). VCSELs are ideal for a number of reasons. First, they operate with very low input power. The laser threshold current is typically below 1 mA for single-transverse-mode devices, and the operating current is under 5 mA, so that only ~ 10 mW of DC power is required to run the device (see Figure 2a). Because of the high modulation bandwidth, the RF power required to produce large first-order optical sidebands is also quite low, about 5 mW, as shown in Figure 2b. Finally, the stable single-mode operation and device reliability are promising features for commercial implementations. Although not yet commercially available, single-transverse-mode VCSELs are made routinely in research labs at the 852 nm D2 transition wavelength of Cs. 16 g

1.2

1 4 •=•

1.0

.. s

12 g 10 £ 8 ^

0

1

2 3 4 5 Laser Current (m A)

(a)

B

a

6 4

a *

4

.a

2

Q

B

0.8

1

0.6

t

T

'

1

'

1

'

»—1

0.4 0.2

0

1 2 3 RFPower(mW)

4

(b)

Figure 2. (a) The VCSEL output power and DC electrical power dissipated in the device as a function of injection current and (b) the power in one first-order optical sideband at 4.6 GHz, as a fraction of the power in the carrier, plotted as a function of RF power injected into the laser.

The microwave transition linewidth, which is normally broadened by collisions of the atoms with the cell walls and the Doppler effect, is reduced with the addition of a buffer gas (typically a few kPa of Ne or N2 for a centimeter-scale cell) to the cell. Larger pressures of buffer gas isolate the Cs atoms more effectively from the cell walls but introduce pressure broadening and reduce the signal strength. In the cells used in the experiment, a combination of Ne and Ar buffer gases, with a total pressure of ~ 5 kPa, was used to reduce the cell's temperature coefficient. A circularly-polarized optical field, created with a quarter-wave-plate between the laser and the cell, was used to excite the CPT resonance. The laser frequency was locked to the optical absorption line to reduce the effects of long-term laser frequency drifts on the clock frequency. A longitudinal magnetic field of ~ 10 pT

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170

was applied to the cell to separate the mF_3=0^mF=4=0 transition from those involving other ground-state Zeeman levels and some magnetic shielding protected the cell from external fields. The laser current was modulated with enough RF power so that about one-half of the optical power was contained in the two firstorder sidebands. Each sideband contained ~ 50 (iW/cm2 in a beam ~ 4 mm in diameter. This was sufficient to see a CPT resonance without the use of a lock-in. Locking to the CPT resonance was accomplished by modulating the frequency of the quartz-crystal oscillator source and demodulating the photodiode's output with a lock-in amplifier and feeding back into the crystal varactor voltage. 4

4.1

Experimental Results

Table-top system

A table-top system was constructed to test the basic method and investigate the limits to the clock performance. In this system a cell of diameter 25 mm and length 20 mm was used. A typical CPT resonance is plotted in Figure 3. The resonance width was 106 Hz (at 4.6 GHz) and the change in power on resonance is about 0.3 % of the total optical power.

i

'

r

100 200 -300 -200 -100 Frequency Detuning (Hz) Figure 3. A typical CPT resonance.

300 Figure 4. Allan deviation for table-top system

When the cell was actively temperature-stabilized and the synthesizer locked to the atomic resonance, the output frequency of the synthesizer at 4.6 GHz was measured as a function of time. The Allan deviation calculated from this time-series data is shown in Figure 4. The short-term fractional frequency instability, characterized by the Allan standard deviation, was 1.6x10"" / \ j r / ( s ) , and bottomed out near 10"12 at 1000 s. The short-term instability was due to several noise sources: laser (shot) noise, linear and non-linear FM-AM conversion noise

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[9], and noise due to optical pumping [11]. The long-term instability is believed to be caused by residual fluctuations in cell temperature, but was not extensively investigated. The fractional shift of the CPT resonance with optical power was ~ 1040/(jiW/cm2), and thefractionalshift with temperature was < 4xl0"!1 l¥L 4.2

Compact System

A compact version of the system was designed and built; a photograph is shown in Figure 5. The support manifold was machined out of a high-permeability material to shield the cellfromexternal magnetic fields. A cell with an inside diameter of 4 mm and length 25 mm was used. The Ml device measured 6.6 cm x 1.6 cm x 1.3 cm, not including connectors. The DC power dissipation was < 30 mW, without thermal control. Laser

Lens

Attenuator

Magnetic shielding

Waveplate

Cell

Photodetector

Figure 5. Compact CPT clock.

Because of the smaller cell size, the CPT resonance, shown in Figure 6, was wider than that of its table-top counterpart, and measured 620 Hz at the operating intensity. We believe that about one-half of this width results from the decay of the polarization diffusion mode due to the cell walls. The remainder is most likely pressure and power broadening. The Allan deviation measured with the system locked is shown in Figure 7. The somewhat larger* short-term instability of 1.3 XlO-10 /\JTl{s) reflects the increased resonance width, while we believe the increased long-term instability is due to the lack of active temperature control of the cell.

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172

1.000 -1000 -500 0 500 1000 Frequency Offset from 4.6 GHz (Hz) T(S)

Figure 6. A CPT resonance in the compact system.

Figure 7. Allan deviation of compact system.

Further Miniaturization A unique advantage of the CPT-resonance clock is the prospect for further miniaturization. In conventional double-resonance clocks, a microwave cavity is used to confine the microwaves in the vicinity of the atoms and to avoid Doppler shifts due to the motion of the atoms along the direction of the field propagation. The microwave cavity must be near the size of the microwave wavelength in order to be resonant, and miniaturization to much below 1 cm appears difficult. In the CPT design, no microwave cavity is required and the miniaturization is limited fundamentally by the wavelength of the optical radiation. This feature is critical for miniaturization to sub-millimeter dimensions. The design of the cell containing the Cs atoms involves a trade-off between size and performance. For a given cell size, there is a specific buffer-gas pressure that optimizes the performance of the clock. At low pressures, collisions of the atoms with the cell walls reduce the atom 10'" Q-factor, while at high pressures, 10' more frequent collisions with the 10* buffer gas atoms do the same. As 10 the cell gets smaller, therefore, the 10 optimum buffer gas pressure ^ ^ — Wall coating 10 Pb*r=13 a increases and the optimized short10 Pbu«.,= 10° kPa P„,„„=1MP 10 term stability of the clock is 10 degraded correspondingly. The 10" 10' 10" 10" 10" 10" effectiveness of wall coatings, Cell Size (m) another technique commonly used Figure 8. Atomic Q-factors for a wall-coated cell to reduce the effect of wall (1000 bounces), and a buffer-gas cell with several collisions on the hyperfine buffer gas pressures. decoherence, also depends on the 7

6

5

kp

4

3

a

2

6

5

4

3

2

1

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173

cell size. The calculated [12] optimum atomic Q-factors are proportional to the cell's characteristic dimension and are plotted in Figure 8. The smaller Q-factors at small dimensions result in increased instability of the frequency reference. The precise value of the Allan deviation depends ultimately on a number of additional factors such as optical power, cell temperature, signal height, and relevant noise sources. 6

Conclusion

A compact frequency reference physics package based on CPT-resonances in Cs vapor has been described. This device measures 6.6 cm x 1.6 cm x 1.3 cm, dissipates less than 30 mW not including temperature control and has a short-term fractional frequency instability of 1.3xl0" 10 /\JT/(S) • Prospects for future miniaturization are excellent, in part because of recent advances in VCSEL technology and because no microwave cavity is required in the CPT design. The main limitation to performance under extreme miniaturization will be the effects of atoms colliding with the walls of a very small cell. However, we believe an instability of less than 10"9 at one second should be possible with a millimeter-scale cell. Such a device is likely to lead to a number of new applications. References | Contribution of NIST. Not subject to copyright. } Also with JILA, The University of Colorado, Boulder, CO. 1. Vig J., Military applications of high-accuracy frequency standards and clocks, IEEE Trans. Ultrason. Ferrelectr. Freq. Control, 40 (1993), pp. 522-7. 2. Kusters J. A. and Adams C. A., Performance requirements of communication base station time standards, RF Design, May, 1999, pp. 28-38. 3. Alzetta G., Gozzini A., Moi L. and Orriols G., An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapour, Nuovo Cim., B 36 (1976), pp. 5-20. 4. Arimondo E. and Orriols G., Nonabsorbing atomic coherences by coherent twophoton transitions in a three-level optical pumping, Lett. Nuovo dm., 17 (1976), pp. 333-8. 5. Thomas J. E., Ezekiel S., Leiby Jr. C.C, Picard R. H. and Willis C. R., Ultrahigh resolution spectroscopy and frequency standards in the microwave and farinfrared regions using optical lasers, Opt. Lett, 6, (1981), pp. 298-300. 6. Cyr N., Tetu M. and Breton M., All-optical microwave frequency standard: a proposal, IEEE Trans Instrum. Meas., 49 (2000), pp. 640-9. 7. Stahler M., Knappe S., Affolderbach C, Kemp W. and Wynands R., Picotesla magnetometry using coherent dark states, Europhys. Lett, 54 (2001), 323-8.

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174

8. Arimondo E., Coherent population trapping in laser spectroscopy. In Progress in Optics XXXV, ed. by E. Wolf (Elsevier Science, Amsterdam, 1996), pp. 257-354. 9. Kitching J., Knappe S., Vukicevic N., Hollberg L., Wynands R. and Weidemann W., A microwave frequency reference based on VCSEL-driven dark-line resonances in Cs vapor, IEEE Trans. Instrum. Meas., 49 (2000), pp. 1313-7. 10. Godone A., Levi F. and Vanier J., Coherent microwave emission without population inversion: a new atomic frequency standard, IEEE Trans. Instrum. Meas., 48 (1999), pp. 504-7. 11. J. Kitching, L. Hollberg, S. Knappe and R. Wynands, Opt. Lett., in press; J. Kitching, H. G. Robinson, L. W. Hollberg, S. Knappe and R. Wynands, J. Opt. Soc. Am. B, in press. 12. Kitching J., and Hollberg L., to be published.

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THE COHERENT POPULATION TRAPPING MASER

A. GODONE, F. LEVI htituto Elettrotecnico Nazionale "G. Ferraris",

Torino, Italy

S. MICALIZIO Politecnico di Torino, Torino, Italy

J. VANIER Universite 4e Montreal, Montreal,

Canada

Coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms under coherent population trapping. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble is taken into account. Moreover, relevant density and propagation effects are described. The case of alkali-metal atoms submitted to a A excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas.

1

Introduction

Since its discovery, the Coherent Population Trapping (CPT) [1] phenomenon has opened a new research field in quantum physics, from both the theoretical and the experimental point of view. Besides its physical interest, CPT has been proposed for applications in many fields, such as atom cooling, magnetometry and atomic frequency standards. CPT is characterized by two basic properties: the trapping of all atoms in the ground state sublevels and the creation of a strong coherence at the hyperfine frequency of the ground state. The first property leads to the presence of the well known dark line in the fluorescence spectrum. The second one creates an oscillating magnetization at the hyperfine frequency responsible for coherent microwave emission when the atomic ensemble is placed inside a cavity. The resulting device has many of the characteristics of a maser and has been named CPT maser [2]. We have carried out several theoretical and experimental studies on the properties of the CPT maser; in particular, these studies were devoted to the physical behavior of the system as well as to its features in view of applications in the frequency standard field. The experimental results and the theoretical analysis are in excellent agreement and give important information about linewidth, line shape, frequency shifts and power output. They also provide guidelines relative to the design parameters involved in the implementation of a CPT maser frequency standard.

175

176

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2

Theory

In this section we report the main results of the CPT maser theory. Throughout this work, we assume that the atomic ensemble may be represented by a three-level model consisting of two ground state levels optically coupled to a common excited state. Obviously, alkali atoms have a more complicated level structure, but the essential physical behavior of the system can be obtained from such a three level approach. We assume the presence of a buffer gas used to reduce wall collisions as well as to increase the transit time of atoms across the laser beam. 2.1

Stimulated

emission.

In the present section, we assume that the atomic medium is optically thin; by this we mean that all the effects related to the atomic density are negligible. The energy level scheme considered in our analysis is shown in Fig.la, while the basic physical arrangement is shown in Fig. lb. Although the following discussion is referred to the Di optical transition of 87 Rb, it can be extended to the general case of A transitions in alkali-metal atoms observed in a cell with buffer gas. CAVITY

CELL 2

5 P„

z LASERS

0) 15 CO, F = 2 5 2S,

l

(N / ^

/

-v- y Jy

•

.

x

K

-'

^ ,"H (RFfield) V

—N.F7?1 HZA i^lrzj •

1 Y,

B0 (a) (b) Figure 1. (a) Three-level system considered in the analysis; u)i and CO2 are the laser angular frequencies and (1)21/271 is the hyperfme frequency (6.834 GHz) shifted by various static perturbations (Zeeman effect, light shift, buffer gas collisions); Ao is the lasers detuning from the optical resonance, (b) Basic physical arrangement. Pi, and P M are the optical transmitted power and the microwave output power. In F i g . l a the d e c a y rate of the excited state T* takes into a c c o u n t s p o n t a n e o u s e m i s s i o n and collisions b e t w e e n the buffer gas and alkali metal a t o m s . T h e relaxation rates Yi a n d y2 of t h e g r o u n d state h y p e r f m e levels p o p u l a t i o n difference and c o h e r e n c e take into a c c o u n t spin e x c h a n g e and buffer gas collisions. T h e master e q u a t i o n d e s c r i b i n g the a t o m i c e n s e m b l e is the g e n e r a l i z e d L i o u v i l l e Bloch equation [3]:

at

in

177

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where: i)p(0 is the density matrix operator containing the information about the relative population of the levels (p ii; i= 1,2,3) and about the coherence induced among them (py, i*j); ii) H(t) is the Hamiltonian operator which describes the atomic interaction with the two lasers producing the A scheme and with the oscillating field in the cavity, as shown in Fig. lb. This field may be applied externally, as in RF double resonance experiments or generated by the atomic ensemble itself. The steady state solution of the Liouville equation shows that when the frequency difference between the two lasers equals the ground state hyperfine frequency, £V=(tt>i-co2)-a>2i=0, the atomic ensemble is driven in a superposition of the ground state sublevels, that is a non absorbing state and, as a consequence, a narrow dark line appears in the fluorescence spectrum (°= p33). Moreover, a strong coherence Pl2 =&\2e ~ i s induced in the ground state itself. This coherence acts as a source of an oscillating magnetic field which leads to coherent stimulated microwave emission when the atoms are coupled to a cavity tuned to the hyperfine frequency. In a formal, way it may be said that the microwave emission is due to the macroscopic magnetization M oscillating at (fli-(02, created by the coherence p^: M(r, t) = Tr(M p) . This magnetization is the "source term" of the classical wave equation for the field //(?) sustained by the cavity [2]: H(7) = -iQLHc(7)\Hc(r)-M(r)dv

(2)

Vc

where Hc(r) is the orthonormal cavity mode, QL the loaded cavity Q-factor and Vc the cavity volume. This field reacts back on the atomic ensemble and causes stimulated emission. However, an analysis of the Liouville equation shows that this feedback is negligible when the Rabi frequency b associated to the microwave emission is small in comparison with the other relaxation and pumping rates. Assuming equal optical angular Rabi frequencies of the two laser fields, that is C0R1 = C0R2 =(0R, and laser radiation fields exactly tuned to the optical transitions, that is AQ = 0, the CPT maser profile is Lorentzian, centered at £1^= 0 with a full width at half maximum (FWHM) equal to Av 1/2 =V Tt \Y2 + c o l/ r *)- I I i s n o t e d t n a t t h e coherent microwave emission takes place without population inversion (Pn = p22=l/2) and without threshold. The CPT maser signal is observed directly at the output of the cavity as in intensity optically pumped (IOP) masers. 2.2 High feedback limit. In this section, we discuss the physical situation where the effect of the cavity feedback on the state of the atomic ensemble is not negligible. The microwave Rabi frequency b is calculated in a self consistent approach in which the energy

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178

dissipated in the cavity is made equal to the energy created by the atoms. The result of this approach is: b = -2/&812 , k being the number of microwave photons emitted per second by each atom . Inserting this expression in (1), we obtain a set of equations describing entirely the phenomenon of stimulated emission in the strong field limit. In this situation, the cavity feedback destroys partially the intrinsic symmetry of the A excitation scheme and new effects are predicted: i) microwave broadening: the microwave field of the cavity strongly couples the hyperfine levels of the ground state producing a broadening of the emission profile; ii) microwave shift: the field stored in the cavity produces an imbalance of the ground state populations even when (ORI = C0R2- This effect shifts the center frequency of the emission profile [2]. 2.3

Propagation and density effects.

The atomic density and the length of the active medium play an important role on the emitted power and on the emission profile of the CPT maser. In particular, the following points have to be considered: i) the travelling wave laser beams used for the A excitation scheme have a relative phase which changes in a significant way along the propagation axis, inside the active medium; ii) the phase of each atomic dipole is referred to the local optical phase difference; iii) due to the fact that the microwave field inside the cavity is a standing wave, each atom is coupled to the microwave field generated by the whole atomic ensemble. We extended the self consistent theoretical approach taking into account the previous points: a new frequency shift arises due to the propagation of the laser fields inside the cell of finite length; moreover, a significant reduction of the linewidth for increasing atomic densities is predicted, even below the natural linewidth limit.

bit) = -2/-}5 12 ( z ,f>- 2, ' lj/x e '' [ *' (z ''>-^ (z '' ) W

LASERS FIELDS

z=0

z=L

Figure 2. The cell containing the atomic medium is divided in m ideal elementary cells (m » 1). The theoretical treatment for a thin medium holds for each cell, but now the phase of each elementary magnetization is referred to the laser fields phase-difference which evolves along z. The total Rabi frequency b associated with the standing microwave field excited in the cavity is given by the sum of all the elementary cells in the limit m—**>. X is the wavelength of the microwave field while Rb in Ne at po 0.20 c m J / s •DNe 0.12cm2/s n diffusion constant of 8 5 R b in Ar at po £>Ar Ne n 55.5 x 1 0 " 2 3 cm 2 decoherence cross section for 8 5 Rb-Ne collisions n 37.1 x 1 0 " 2 3 cm 2 decoherence cross section for 8 5 Rb-Ar collisions 85 6 2.54 x 10~ 1 4 cm 2 spin-exchange cross section for R b 0"se

A minimization of Eq. (1) using pAt/PNe ~ 0.87 and the numerical values from Table 1 gives the optimal partial pressures p\T ss 16 mbar and p^e « 19 mbar. These parameters yield a calculated DR linewidth of 8u = 72/^ « 17 Hz. The uncertainty is, however, large due to the uncertainties of the experimentally obtained decoherence cross sections and diffusion constants. The hfs pressure shift (several kHz) is of great concern in gas-cell-based atomic clocks. The pressure uncertainty, typically 1 % in commercial cells, makes it necessary to characterize the frequency of each cell individually, making this type of an atomic clock a secondary frequency standard. Because of the 400-MHz pressure broadening 12 the excited hyperfine states are overlapping. There will thus be an additional CPT contribution

186

from the F' = 2 state as well as one-photon transitions to F' = 1 and F' = 4. This complicates the analysis of the CPT spectra 13 and the light shift. 9

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3

Experimental Setup

The laser source used in this work is a 780 nm commercial edge-emitting diode laser equipped with an integrated microlens (Blue Sky Research PS026). The optical feedback from the closely mounted microlens improves the sidemode suppression ratio, the beam geometry, and the frequency tunability. Edge-emitting diode lasers have intrinsically low intensity noise, which is beneficial as intensity noise at the detection frequency essentially determines the signal-to-noise ratio. The measured intensity noise of the laser is — 130dB/Hz at the measurement frequency. Since the two CPT laser modes are generated from the same laser source through frequency modulation, the frequency noise of the modes is nearly perfectly correlated and has no effect on the decay rate of the ground-state coherence. x However, the frequency noise can be converted to intensity noise in the resonance 14 and thus deteriorate the signal-to-noise ratio of detection. In this case the frequency noise is determined by the properties of the laser diode, as the optical feedback from the microlens is too weak to narrow the linewidth of the laser diode. Fortunately the high output power of the laser diode (~20mW) and the properties of its cavity yield a relatively small fundamental linewidth of 2 MHz. The power of the first-order red sideband used as WL2 was 30 % of the carrier power. A laser frequency stabilization scheme similar to the one described in Ref. 15 is used to lock the laser frequency to the cross-over resonance between the transitions \F = 2) ->• \F' = 1) and |F = 2) -> \F' = 2) of the D 2 line. This resonance has been used as it gives the strongest signal and partially compensates the -130 MHz pressure shift 12 caused by the buffer gas. The experimental setup is schematically shown in Fig. 2. The clock part of the optical setup consists of a Rb cell, polarization and beam-expansion optics and a photodetector. The Rb cell is placed inside a long solenoid which in turn is enclosed by a magnetic shield. A lens is used to collect the light on a large-area, high-quantum yield (90 %) PIN photodiode. 4 4-1

Measurement Results Dark Resonances

The good noise properties of the laser source and the expanded beam allow detection of dark resonances using very low intensities and thus very low

187 Tofrequsncy

h

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3,036 GHz rh

LD HL

* « PBS *G ND

M

l"EEp3-l