The quantum physics of atomic frequency standards : recent developments

478 Pages·2016·21.285 MB·English

by  Tomescu, Cipriana, Vanier, Jacques

The Quantum
Physics of
Atomic
Frequency
Standards
Recent Developments
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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
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Version Date: 20150617
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Contents
Preface....................................................................................................................xiii
Introduction ............................................................................................................xvii
Authors ....................................................................................................................xix
Chapter 1 Microwave Atomic Frequency Standards: Review and Recent
Developments .......................................................................................1
1.1 Classical Atomic Frequency Standards .....................................2
1.1.1 Cs Beam Frequency Standard ......................................2
1.1.1.1 Description of the Approach Using
Magnetic State Selection ..............................3
1.1.1.2 Review of Frequency Shifts and Accuracy ....7
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 2 Recent Advances in Atomic Physics That Have Impact
on Atomic Frequency Standards Development ................................101
2.1 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
2.2 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
2.3 Laser Optical Pumping ..........................................................119
2.3.1 Rate Equations .........................................................120
2.3.2 Field Equation and Coherence .................................122
2.4 Coherent Population Trapping ...............................................127
2.4.1 Physics of the CPT Phenomenon .............................129
2.4.2 Basic Equations ........................................................131
2.5 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
Contents vii
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 3 Microwave Frequency Standards Using New Physics .....................191
3.1 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
3.2 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 Magnetic Field ..........................................221
3.2.4.4 Temperature Control .................................221
3.2.4.5 Capture and Selection Zone ......................221
3.2.4.6 Detection Zone .........................................221
3.2.4.7 Supporting Systems ..................................221
3.2.4.8 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
3.3 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
3.4 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
Contents ix
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 Collisions and Scattering Length ....................337
Appendix 3.C: Optical Absorption of Polarized Laser Radiation
Including Optical Pumping ..............................................................338
Appendix 3.D: Basic CPT Maser Theory ........................................341