Preface |
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xiii | |
Introduction |
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xvii | |
Authors |
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xix | |
Chapter 1 Microwave Atomic Frequency Standards: Review and Recent Developments |
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1 | (100) |
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1.1 Classical Atomic Frequency Standards |
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2 | (80) |
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1.1.1 Cs Beam Frequency Standard |
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2 | (31) |
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1.1.1.1 Description of the Approach Using Magnetic State Selection |
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3 | (4) |
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1.1.1.2 Review of Frequency Shifts and Accuracy |
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7 | (8) |
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1.1.1.3 Frequency Stability of the Cs Beam Standard |
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15 | (1) |
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1.1.1.4 Recent Accomplishments |
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16 | (17) |
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33 | (36) |
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1.1.2.1 Active Hydrogen Maser |
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33 | (15) |
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1.1.2.2 Passive Hydrogen Maser |
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48 | (5) |
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1.1.2.3 Frequency Stability of the Hydrogen Maser |
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53 | (4) |
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1.1.2.4 State of the Art of Recent Developments and Realizations |
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57 | (12) |
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1.1.3 Optically Pumped Rb Frequency Standards |
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69 | (13) |
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1.1.3.1 General Description |
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69 | (2) |
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1.1.3.2 State-of-the-Art Development |
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71 | (11) |
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1.2 Other Atomic Microwave Frequency Standards |
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82 | (11) |
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1.2.1 199Hg+ Ion Frequency Standard |
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83 | (7) |
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1.2.1.1 General Description |
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83 | (2) |
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85 | (3) |
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88 | (2) |
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1.2.2 Other Ions in a Paul Trap |
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90 | (12) |
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1.2.2.1 171yb+ and 173Yb+ Ion Microwave Frequency Standards |
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91 | (1) |
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1.2.2.2 201Hg+ Ion Microwave Frequency Standard |
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92 | (1) |
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1.3 On the Limits of Classical Microwave Atomic Frequency Standards |
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93 | (1) |
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Appendix 1.A: Formula for Second-Order Doppler Shift |
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94 | (1) |
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Appendix 1.B: Phase Shift between the Arms of Ramsey Cavity |
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95 | (1) |
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Appendix 1.C: Square Wave Frequency Modulation and Frequency Shifts |
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95 | (2) |
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Appendix 1.D: Ring Cavity Phase Shift |
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97 | (1) |
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Appendix 1.E: Magnetron Cavity |
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98 | (3) |
Chapter 2 Recent Advances in Atomic Physics That Have Impact on Atomic Frequency Standards Development |
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101 | (90) |
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2.1 Solid-State Diode Laser |
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102 | (7) |
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2.1.1 Basic Principle of Operation of a Laser Diode |
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102 | (3) |
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2.1.2 Basic Characteristics of the Semiconductor Laser Diode |
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105 | (1) |
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2.1.3 Types of Laser Diodes |
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106 | (2) |
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2.1.4 Other Types of Lasers Used in Special Situations |
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108 | (1) |
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2.2 Control of Wavelength and Spectral Width of Laser Diodes |
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109 | (10) |
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2.2.1 Line Width Reduction |
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109 | (7) |
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2.2.1.1 Simple Optical Feedback |
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109 | (1) |
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2.2.1.2 Extended Cavity Approach |
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109 | (3) |
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2.2.1.3 Feedback from High-Q Optical Cavities |
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112 | (1) |
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2.2.1.4 Electrical Feedback |
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112 | (1) |
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112 | (1) |
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2.2.1.6 Locking the Laser to an Ultra-Stable Cavity |
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113 | (3) |
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2.2.2 Laser Frequency Stabilization Using an Atomic Resonance Line |
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116 | (3) |
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2.2.2.1 Locking the Laser Frequency to Linear Optical Absorption |
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116 | (1) |
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2.2.2.2 Locking the Laser Frequency to Saturated Absorption |
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117 | (2) |
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2.3 Laser Optical Pumping |
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119 | (8) |
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120 | (2) |
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2.3.2 Field Equation and Coherence |
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122 | (5) |
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2.4 Coherent Population Trapping |
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127 | (9) |
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2.4.1 Physics of the CPT Phenomenon |
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129 | (2) |
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131 | (5) |
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2.5 Laser Cooling of Atoms |
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136 | (53) |
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2.5.1 Atom—Radiation Interaction |
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138 | (20) |
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2.5.1.1 Effect of a Photon on Atom External Properties: Semi-Classical Approach |
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138 | (5) |
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2.5.1.2 Quantum Mechanical Approach |
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143 | (15) |
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2.5.2 Effect of Fluctuations in Laser Cooling and Its Limit |
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158 | (2) |
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2.5.3 Cooling below Doppler Limit: Sisyphus Cooling |
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160 | (7) |
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2.5.3.1 Physics of Sisyphus Cooling |
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160 | (4) |
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164 | (1) |
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2.5.3.3 Friction Coefficient |
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165 | (1) |
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2.5.3.4 Cooling Limit Temperature |
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166 | (1) |
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166 | (1) |
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2.5.3.6 Sub-Recoil Cooling |
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167 | (1) |
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2.5.4 Magneto-Optical Trap |
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167 | (3) |
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2.5.5 Other Experimental Techniques in Laser Cooling and Trapping |
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170 | (22) |
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2.5.5.1 Laser Atom-Slowing Using a Frequency Swept Laser System: Chirp Laser Slowing |
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171 | (2) |
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2.5.5.2 Laser Atom-Slowing Using Zeeman Effect: Zeeman Slower |
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173 | (4) |
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2.5.5.3 2D Magneto-Optical Trap |
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177 | (3) |
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2.5.5.4 Isotropic Cooling |
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180 | (3) |
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2.5.5.5 Optical Lattice Approach |
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183 | (6) |
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Appendix 2.A: Laser Cooling—Energy Considerations |
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189 | (2) |
Chapter 3 Microwave Frequency Standards Using New Physics |
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191 | (154) |
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3.1 Cs Beam Frequency Standard |
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192 | (18) |
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3.1.1 Optically Pumped Cs Beam Frequency Standard |
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192 | (8) |
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3.1.1.1 General Description |
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192 | (2) |
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3.1.1.2 Frequency Shifts and Accuracy |
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194 | (3) |
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3.1.1.3 Experimental Determination of Those Shifts |
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197 | (1) |
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3.1.1.4 Frequency Stability |
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198 | (2) |
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3.1.1.5 Field Application |
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200 | (1) |
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3.1.2 CPT Approach in a Beam |
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200 | (8) |
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3.1.2.1 General Description |
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200 | (1) |
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201 | (5) |
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3.1.2.3 Experimental Results |
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206 | (2) |
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3.1.3 Classical Cs Beam Standard Using Beam Cooling |
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208 | (2) |
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3.2 Atomic Fountain Approach |
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210 | (48) |
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3.2.1 In Search of a Solution |
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210 | (1) |
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3.2.2 General Description of the Cs Fountain |
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211 | (2) |
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3.2.3 Functioning of the Cs Fountain |
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213 | (6) |
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3.2.3.1 Formation of the Cooled Atomic Cloud: Zone A |
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213 | (4) |
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3.2.3.2 Preparation of the Atoms: Zone B |
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217 | (1) |
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3.2.3.3 Interrogation Region: Zone C |
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218 | (1) |
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3.2.3.4 Free Motion: Zone D |
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218 | (1) |
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3.2.3.5 Detection Region: Zone E |
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218 | (1) |
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3.2.4 Physical Construction of the Cs Fountain |
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219 | (4) |
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219 | (1) |
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220 | (1) |
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221 | (1) |
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3.2.4.4 Temperature Control |
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221 | (1) |
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3.2.4.5 Capture and Selection Zone |
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221 | (1) |
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221 | (1) |
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3.2.4.7 Supporting Systems |
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221 | (1) |
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3.2.4.8 Advantages and Disadvantages of a Pulsed Fountain |
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222 | (1) |
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3.2.5 Frequency Stability of the Cs Fountain |
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223 | (3) |
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3.2.5.1 Photon Shot Noise |
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224 | (1) |
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3.2.5.2 Quantum Projection Noise |
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225 | (1) |
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225 | (1) |
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3.2.5.4 Reference Oscillator Noise: Dicke Effect |
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225 | (1) |
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3.2.6 Rubidium and Dual Species Fountain Clock |
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226 | (3) |
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3.2.7 Frequency Shifts and Biases Present in the Fountain |
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229 | (22) |
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3.2.7.1 Second-Order Zeeman Shift |
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230 | (2) |
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3.2.7.2 Black Body Radiation Shift |
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232 | (5) |
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237 | (3) |
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3.2.7.4 Cavity Phase Shift |
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240 | (2) |
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242 | (5) |
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3.2.7.6 Microwave Spectral Purity |
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247 | (1) |
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3.2.7.7 Microwave Leakage |
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247 | (1) |
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3.2.7.8 Relativistic Effects |
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248 | (1) |
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249 | (1) |
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3.2.7.10 Conclusion on Frequency Shifts and Accuracy |
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250 | (1) |
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3.2.8 An Alternative Cold Caesium Frequency Standard: The Continuous Fountain |
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251 | (6) |
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252 | (1) |
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3.2.8.2 Interrogation Zone, Microwave Cavity |
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253 | (2) |
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3.2.8.3 Preliminary Results |
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255 | (2) |
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3.2.9 Cold Atom PHARAO Cs Space Clock |
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257 | (1) |
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3.3 Isotropic Cooling Approach |
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258 | (4) |
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3.3.1 External Cavity Approach: CHARLI |
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258 | (2) |
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3.3.2 Approach Integrating Reflecting Sphere and Microwave Cavity: HORACE |
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260 | (1) |
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3.3.3 Different HORACE Approach |
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261 | (1) |
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3.4 Room Temperature Rb Standard Approach Using Laser Optical Pumping |
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262 | (38) |
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3.4.1 Contrast, Line Width, and Light Shift |
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263 | (9) |
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3.4.2 Effect of Laser Radiation Beam Shape |
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272 | (1) |
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3.4.3 Expectations Relative to Short-Term Frequency Stability |
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273 | (1) |
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3.4.4 Review of Experimental Results on Signal Size, Line Width, and Frequency Stability |
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273 | (5) |
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278 | (9) |
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278 | (1) |
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3.4.5.2 Magnetic Field Shift |
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279 | (1) |
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279 | (5) |
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3.4.5.4 Spin-Exchange Frequency Shift |
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284 | (1) |
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3.4.5.5 Microwave Power Shift |
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285 | (1) |
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286 | (1) |
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3.4.6 Impact of Laser Noise and Instability on Clock Frequency Stability |
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287 | (10) |
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3.4.6.1 Spectral Width, Phase Noise, and Intensity Noise of Laser Diodes |
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288 | (2) |
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3.4.6.2 Impact of Laser Noise on Clock Short-Term Frequency Stability |
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290 | (5) |
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3.4.6.3 Medium- and Long-Term Frequency Stability |
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295 | (2) |
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3.4.7 Other Approaches Using Laser Optical Pumping with a Sealed Cell |
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297 | (3) |
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297 | (1) |
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3.4.7.2 Laser Pulsing Approach |
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297 | (2) |
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3.4.7.3 Wall-Coated Cell Approach |
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299 | (1) |
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300 | (24) |
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3.5.1 Sealed Cell with a Buffer Gas in Continuous Mode: Passive Frequency Standard |
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300 | (15) |
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3.5.1.1 Signal Amplitude and Line Width |
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302 | (5) |
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3.5.1.2 Practical Implementation and Its Characteristics |
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307 | (8) |
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3.5.2 Active Approach in a Cell: The CPT Maser |
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315 | (7) |
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3.5.2.1 Basic CPT Maser Theory |
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315 | (3) |
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3.5.2.2 Frequency Stability |
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318 | (2) |
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320 | (2) |
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3.5.3 Techniques for Improving S/N Ratio in the Passive IOP and CPT Clock Approach |
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322 | (1) |
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3.5.4 CPT in Laser-Cooled Ensemble for Realizing a Frequency Standard |
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323 | (1) |
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3.6 Laser-Cooled Microwave Ion Clocks |
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324 | (5) |
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3.6.1 9Be+ 303 MHz Radio-Frequency Standard |
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325 | (2) |
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3.6.2 113Cd+ and 111Cd+ Ion Trap |
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327 | (1) |
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3.6.3 171Yb+ Laser-Cooled Microwave Frequency Standard |
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328 | (1) |
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Appendix 3.A: Frequency Stability of an Atomic Fountain |
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329 | (8) |
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333 | (1) |
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3.A.2 Quantum Projection Noise |
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334 | (3) |
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Appendix 3.B: Cold Collisions and Scattering Length |
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337 | (1) |
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Appendix 3.C: Optical Absorption of Polarized Laser Radiation Including Optical Pumping |
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338 | (3) |
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Appendix 3.D: Basic CPT Maser Theory |
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341 | (4) |
Chapter 4 Optical Frequency Standards |
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345 | (56) |
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4.1 Early Approach Using Absorption Cells |
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347 | (2) |
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349 | (2) |
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351 | (1) |
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4.4 Single Ion Optical Clocks |
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352 | (25) |
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352 | (5) |
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4.4.2 Outline of Particular Implementations with Individual Ions |
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357 | (9) |
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357 | (2) |
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4.4.2.2 40Ca+ (I = 0) and 43Ca+ (1 = 7/2) |
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359 | (2) |
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4.4.2.3 87Sr+ (I = 9/2) and 88Sr+ (1 = 0) |
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361 | (1) |
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362 | (1) |
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4.4.2.5 137Ba+ (I = 3/2) and 1"Ba+ (1 = 0) |
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363 | (1) |
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4.4.2.6 171Yb+ (I = 1/2), 172Yb+ (I = 0), and 13Yb+ (I = 5/2) |
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364 | (2) |
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4.4.2.7 198Hg+ (I = 0) and 199Hg+ (1 = 1/2) |
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366 | (1) |
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4.4.3 Systematic Frequency Shifts in Single Ion Clocks |
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366 | (11) |
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366 | (2) |
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368 | (3) |
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4.4.3.3 Biases due to the Presence of Electric Fields |
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371 | (6) |
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4.5 Optical Lattice Neutral Atoms Clock |
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377 | (20) |
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377 | (9) |
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4.5.1.1 Trapping Characteristics |
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382 | (1) |
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383 | (1) |
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4.5.1.3 Atom Localization |
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383 | (1) |
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384 | (1) |
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385 | (1) |
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4.5.2 Type of Atoms Used in Optical Lattice Clocks |
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386 | (5) |
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386 | (1) |
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387 | (2) |
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389 | (1) |
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390 | (1) |
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391 | (1) |
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4.5.3 Important Frequency Biases |
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391 | (4) |
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391 | (1) |
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392 | (1) |
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4.5.3.3 Lattice Light Shift |
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393 | (1) |
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394 | (1) |
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4.5.4 Frequency Stability of an Optical Lattice Clock |
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395 | (1) |
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4.5.5 Practical Realizations |
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395 | (2) |
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4.6 Frequency Measurement of Optical Clocks |
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397 | (4) |
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398 | (1) |
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4.6.2 Clock Frequencies and Frequency Stabilities Realized |
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399 | (2) |
Chapter 5 Summary, Conclusion, and Reflections |
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401 | (14) |
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5.1 Accuracy and Frequency Stability |
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402 | (2) |
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5.2 Selected Applications of Atomic Frequency Standards |
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404 | (8) |
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5.2.1 The SI: Towards a Redefinition of the Second |
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405 | (2) |
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5.2.2 Tests of Fundamental Physical Laws |
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407 | (3) |
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5.2.2.1 Fundamental Constants |
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407 | (1) |
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5.2.2.2 Time Dilation and Gravitational Red Shift |
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408 | (1) |
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5.2.2.3 Fundamental Physics in Space |
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409 | (1) |
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5.2.3 Clocks for Astronomy and Earth Science |
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410 | (2) |
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410 | (1) |
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5.2.3.2 Deep Space Network |
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410 | (1) |
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5.2.3.3 Earth Clocks Network |
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410 | (1) |
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5.2.3.4 Navigation Systems |
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411 | (1) |
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412 | (3) |
References |
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415 | (42) |
Index |
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457 | |