The quantum physics of atomic frequency standarda

The Quantum Physics of Atomic Frequency Standards Recent Developments This page intentionally left blank The Quantum Physics of Atomic Frequency Standards Recent Developments Jacques Vanier Université de Montréal, Montréal, Canada Cipriana Tomescu Université de Montréal, Montréal, Canada CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20150617 International Standard Book Number-13: 978-1-4665-7697-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xiii Introduction xvii Authors xix Chapter Microwave Atomic Frequency Standards: Review and Recent Developments .1 1.1 Classical Atomic Frequency Standards .2 1.1.1 Cs Beam Frequency Standard 1.1.1.1 Description of the Approach Using Magnetic State Selection 1.1.1.2 Review of Frequency Shifts and Accuracy 1.1.1.3 Frequency Stability of the Cs Beam Standard 15 1.1.1.4 Recent Accomplishments 16 1.1.2 Hydrogen Maser 33 1.1.2.1 Active Hydrogen Maser 33 1.1.2.2 Passive Hydrogen Maser 48 1.1.2.3 Frequency Stability of the Hydrogen Maser 53 1.1.2.4 State of the Art of Recent Developments and Realizations 57 1.1.3 Optically Pumped Rb Frequency Standards 69 1.1.3.1 General Description 69 1.1.3.2 State-of-the-Art Development 71 1.2 Other Atomic Microwave Frequency Standards 82 1.2.1 199Hg+ Ion Frequency Standard 83 1.2.1.1 General Description 83 1.2.1.2 Frequency Shifts 85 1.2.1.3 Linear Trap 88 1.2.2 Other Ions in a Paul Trap 90 1.2.2.1 171Yb+ and 173Yb+ Ion Microwave Frequency Standards 91 1.2.2.2 201Hg+ Ion Microwave Frequency Standard 92 1.3 On the Limits of Classical Microwave Atomic Frequency Standards 93 Appendix 1.A: Formula for Second-Order Doppler Shift 94 Appendix 1.B: Phase Shift between the Arms of Ramsey Cavity 95 v vi Contents Appendix 1.C: Square Wave Frequency Modulation and Frequency Shifts 95 Appendix 1.D: Ring Cavity Phase Shift 97 Appendix 1.E: Magnetron Cavity 98 Chapter Recent Advances in Atomic Physics That Have Impact on Atomic Frequency Standards Development 101 2.1 2.2 2.3 2.4 2.5 Solid-State Diode Laser 102 2.1.1 Basic Principle of Operation of a Laser Diode 102 2.1.2 Basic Characteristics of the Semiconductor Laser Diode 105 2.1.3 Types of Laser Diodes 106 2.1.4 Other Types of Lasers Used in Special Situations 108 Control of Wavelength and Spectral Width of Laser Diodes 109 2.2.1 Line Width Reduction 109 2.2.1.1 Simple Optical Feedback 109 2.2.1.2 Extended Cavity Approach 109 2.2.1.3 Feedback from High-Q Optical Cavities 112 2.2.1.4 Electrical Feedback 112 2.2.1.5 Other Approaches 112 2.2.1.6 Locking the Laser to an Ultra-Stable Cavity 113 2.2.2 Laser Frequency Stabilization Using an Atomic Resonance Line 116 2.2.2.1 Locking the Laser Frequency to Linear Optical Absorption 116 2.2.2.2 Locking the Laser Frequency to Saturated Absorption 117 Laser Optical Pumping 119 2.3.1 Rate Equations 120 2.3.2 Field Equation and Coherence 122 Coherent Population Trapping 127 2.4.1 Physics of the CPT Phenomenon 129 2.4.2 Basic Equations 131 Laser Cooling of Atoms 136 2.5.1 Atom–Radiation Interaction 138 2.5.1.1 Effect of a Photon on Atom External Properties: Semi-Classical Approach 138 2.5.1.2 Quantum Mechanical Approach 143 2.5.2 Effect of Fluctuations in Laser Cooling and Its Limit 158 2.5.3 Cooling below Doppler Limit: Sisyphus Cooling 160 2.5.3.1 Physics of Sisyphus Cooling 160 2.5.3.2 Capture Velocity 164 vii Contents 2.5.3.3 Friction Coefficient 165 2.5.3.4 Cooling Limit Temperature 166 2.5.3.5 Recoil Limit 166 2.5.3.6 Sub-Recoil Cooling 167 2.5.4 Magneto-Optical Trap 167 2.5.5 Other Experimental Techniques in Laser Cooling and Trapping 170 2.5.5.1 Laser Atom-Slowing Using a Frequency Swept Laser System: Chirp Laser Slowing 171 2.5.5.2 Laser Atom-Slowing Using Zeeman Effect: Zeeman Slower 173 2.5.5.3 2D Magneto-Optical Trap 177 2.5.5.4 Isotropic Cooling 180 2.5.5.5 Optical Lattice Approach 183 Appendix 2.A: Laser Cooling—Energy Considerations 189 Chapter Microwave Frequency Standards Using New Physics 191 3.1 3.2 Cs Beam Frequency Standard 192 3.1.1 Optically Pumped Cs Beam Frequency Standard 192 3.1.1.1 General Description 192 3.1.1.2 Frequency Shifts and Accuracy 194 3.1.1.3 Experimental Determination of Those Shifts 197 3.1.1.4 Frequency Stability 198 3.1.1.5 Field Application 200 3.1.2 CPT Approach in a Beam 200 3.1.2.1 General Description 200 3.1.2.2 Analysis 201 3.1.2.3 Experimental Results 206 3.1.3 Classical Cs Beam Standard Using Beam Cooling 208 Atomic Fountain Approach 210 3.2.1 In Search of a Solution 210 3.2.2 General Description of the Cs Fountain 211 3.2.3 Functioning of the Cs Fountain 213 3.2.3.1 Formation of the Cooled Atomic Cloud: Zone A 213 3.2.3.2 Preparation of the Atoms: Zone B 217 3.2.3.3 Interrogation Region: Zone C 218 3.2.3.4 Free Motion: Zone D 218 3.2.3.5 Detection Region: Zone E 218 3.2.4 Physical Construction of the Cs Fountain 219 3.2.4.1 Vacuum Chamber 219 3.2.4.2 Microwave Cavity 220 viii Contents 3.2.4.3 3.2.4.4 3.2.4.5 3.2.4.6 3.2.4.7 3.2.4.8 3.3 3.4 Magnetic Field 221 Temperature Control 221 Capture and Selection Zone 221 Detection Zone 221 Supporting Systems 221 Advantages and Disadvantages of a Pulsed Fountain 222 3.2.5 Frequency Stability of the Cs Fountain 223 3.2.5.1 Photon Shot Noise 224 3.2.5.2 Quantum Projection Noise 225 3.2.5.3 Electronic Noise 225 3.2.5.4 Reference Oscillator Noise: Dicke Effect 225 3.2.6 Rubidium and Dual Species Fountain Clock 226 3.2.7 Frequency Shifts and Biases Present in the Fountain 229 3.2.7.1 Second-Order Zeeman Shift 230 3.2.7.2 Black Body Radiation Shift 232 3.2.7.3 Collision Shift 237 3.2.7.4 Cavity Phase Shift 240 3.2.7.5 Cavity Pulling 242 3.2.7.6 Microwave Spectral Purity 247 3.2.7.7 Microwave Leakage 247 3.2.7.8 Relativistic Effects 248 3.2.7.9 Other Shifts 249 3.2.7.10 Conclusion on Frequency Shifts and Accuracy 250 3.2.8 An Alternative Cold Caesium Frequency Standard: The Continuous Fountain 251 3.2.8.1 Light Trap 252 3.2.8.2 Interrogation Zone, Microwave Cavity 253 3.2.8.3 Preliminary Results 255 3.2.9 Cold Atom PHARAO Cs Space Clock 257 Isotropic Cooling Approach 258 3.3.1 External Cavity Approach: CHARLI 258 3.3.2 Approach Integrating Reflecting Sphere and Microwave Cavity: HORACE 260 3.3.3 Different HORACE Approach 261 Room Temperature Rb Standard Approach Using Laser Optical Pumping 262 3.4.1 Contrast, Line Width, and Light Shift 263 3.4.2 Effect of Laser Radiation Beam Shape 272 3.4.3 Expectations Relative to Short-Term Frequency Stability 273 3.4.4 Review of Experimental Results on Signal Size, Line Width, and Frequency Stability 273 ix Contents 3.4.5 Frequency Shifts 278 3.4.5.1 Buffer Gas Shift 278 3.4.5.2 Magnetic Field Shift 279 3.4.5.3 Light Shift 279 3.4.5.4 Spin-Exchange Frequency Shift .284 3.4.5.5 Microwave Power Shift 285 3.4.5.6 Cavity Pulling 286 3.4.6 Impact of Laser Noise and Instability on Clock Frequency Stability 287 3.4.6.1 Spectral Width, Phase Noise, and Intensity Noise of Laser Diodes 288 3.4.6.2 Impact of Laser Noise on Clock Short-Term Frequency Stability 290 3.4.6.3 Medium- and Long-Term Frequency Stability 295 3.4.7 Other Approaches Using Laser Optical Pumping with a Sealed Cell 297 3.4.7.1 Maser Approach 297 3.4.7.2 Laser Pulsing Approach 297 3.4.7.3 Wall-Coated Cell Approach 299 3.5 CPT Approach .300 3.5.1 Sealed Cell with a Buffer Gas in Continuous Mode: Passive Frequency Standard 300 3.5.1.1 Signal Amplitude and Line Width 302 3.5.1.2 Practical Implementation and Its Characteristics 307 3.5.2 Active Approach in a Cell: The CPT Maser 315 3.5.2.1 Basic CPT Maser Theory 315 3.5.2.2 Frequency Stability 318 3.5.2.3 Frequency Shifts 320 3.5.3 Techniques for Improving S/N Ratio in the Passive IOP and CPT Clock Approach 322 3.5.4 CPT in Laser-Cooled Ensemble for Realizing a Frequency Standard 323 3.6 Laser-Cooled Microwave Ion Clocks 324 3.6.1 9Be+ 303 MHz Radio-Frequency Standard 325 3.6.2 113Cd+ and 111Cd+ Ion Trap 327 3.6.3 171Yb+ Laser-Cooled Microwave Frequency Standard 328 Appendix 3.A: Frequency Stability of an Atomic Fountain 329 3.A.1 Shot Noise 333 3.A.2 Quantum Projection Noise 334 Appendix 3.B: Cold 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