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Tables of Contents for The Quantum Beat
Chapter/Section Title
Page #
Page Count
Preface
vii
Chapter 1. Celestial and Mechanical Clocks
1
22
1.1 Cyclic Events in Nature
1
1
1.2 The Calendar
2
1
1.3 Solar Eclipses as Time Markers
3
2
1.4 The Tides
5
2
1.5 The Sidereal Day
7
1
1.6 The Precession of the Equinoxes
8
1
1.7 The Sundial
9
1
1.8 The Astrolabe
10
2
1.9 Water Clocks
12
2
1.10 Tower Clocks
14
2
1.11 The Pendulum Clock
16
3
1.12 The Spring--Balance-Wheel Clock
19
4
Chapter 2. Oscillations and Fourier Analysis
23
24
2.1 Oscillatory Motion in Matter
23
1
2.2 Simple Harmonic Motion
24
2
2.3 Forced Oscillations: Resonance
26
3
2.4 Waves in Extended Media
29
3
2.5 Wave Dispersion
32
1
2.6 Linear and Nonlinear Media
33
2
2.7 Normal Modes of Vibration
35
2
2.8 Parametric Excitations
37
2
2.9 Fourier Analysis
39
4
2.10 Coupled Oscillations
43
4
Chapter 3. Oscillators
47
16
3.1 Feedback in Amplifiers
47
3
3.2 Conditions for Oscillation
50
1
3.3 Resonators
51
3
3.4 The Klystron Microwave Tube
54
2
3.5 Oscillators at Optical Frequency
56
2
3.6 Stability of Oscillators: Noise
58
5
Chapter 4. Quartz Clocks
63
26
4.1 Historical Antecedents
63
3
4.2 Properties and Structure of Crystalline Quartz
66
5
4.3 Modes of Vibration of a Quartz Plate
71
2
4.4 X-Ray Crystallography
73
2
4.5 Fabrication of Quartz Resonators
75
1
4.6 Factors Affecting the Resonance Frequency
76
2
4.7 The Quartz Resonator as a Circuit Element
78
2
4.8 Frequency Stability
80
4
4.9 Frequency/Time Measurement
84
4
4.10 Quartz Watches
88
1
Chapter 5. The Language of Electrons, Atoms, and Quanta
89
28
5.1 Classical Lorentz Theory
89
1
5.2 Spectrum of Blackbody Radiation
90
1
5.3 The Quantum of Radiation: The Photon
91
1
5.4 Bohr's Theory of the Hydrogen Atom
92
2
5.5 The Schrodinger Wave Equation
94
2
5.6 Quantum Numbers of Atomic States
96
2
5.7 The Vector Model
98
1
5.8 The Shell Structure of Electron States
99
2
5.9 The Pauli Exclusion Principle
101
2
5.10 Spectroscopic Notation
103
1
5.11 The Hyperfine Interaction
104
5
5.12 Electrons in Solids: The Band Theory
109
8
Chapter 6. Magnetic Resonance
117
24
6.1 Introduction
117
1
6.2 Atomic Magnetism
117
1
6.3 The Zeeman Effect
118
4
6.4 Gyroscopic Motion in a Magnetic Field
122
1
6.5 Inducing Transitions
123
4
6.6 Motion of Global Moment: The Bloch Theory
127
1
6.7 Production of Global Polarization
128
13
Chapter 7. Corrections to Observed Atomic Resonance
141
20
7.1 Homogeneous and Inhomogeneous Broadening
142
2
7.2 The Special Theory of Relativity
144
2
7.3 The Doppler Effect
146
2
7.4 The Thermal Doppler Line Shape
148
2
7.5 Sub-Doppler Line Widths: the Dicke Effect
150
3
7.6 The General Theory of Relativity
153
6
7.7 Conclusion
159
2
Chapter 8. The Rubidium Clock
161
18
8.1 The Reference Hyperfine Transition
161
2
8.2 The Breit-Rabi Formula
163
1
8.3 Optical Pumping of Hyperfine Populations
164
3
8.4 Optical Hyperfine Pumping: Use of an Isotopic Filter
167
2
8.5 The Use of Buffer Gases
169
3
8.6 Light Shifts in the Reference Frequency
172
1
8.7 Rubidium Frequency Control of Quartz Oscillator
173
3
8.8 Frequency Stability of the Rubidium Standard
176
2
8.9 The Miniaturization of Atomic Clocks
178
1
Chapter 9. The Classical Cesium Standard
179
26
9.1 Definition of the Unit of Time
179
1
9.2 Implementation of the Definition: The Cesium Standard
180
3
9.3 The Physical Design
183
7
9.4 The Ramsey Separated Field
190
6
9.5 Detection of Transitions
196
2
9.6 Frequency-Lock of Flywheel Oscillator to Cesium
198
3
9.7 Corrections to the Observed Cs Frequency
201
4
Chapter 10. Atomic and Molecular Oscillators: Masers
205
18
10.1 The Ammonia Maser
205
1
10.2 Basic Elements of a Beam Maser
206
1
10.3 Inversion Spectrum in NH(3)
207
3
10.4 The Electrostatic State Selector
210
4
10.5 Stimulated Radiation in the Cavity
214
2
10.6 Threshold for Sustained Oscillation
216
1
10.7 Sources of Frequency Instability
217
4
10.8 The Rubidium Maser
221
2
Chapter 11. The Hydrogen Maser
223
32
11.1 Introduction
223
2
11.2 The Hyperfine Structure of H Ground State
225
3
11.3 Principles of the Hydrogen Maser
228
7
11.4 Physical Design of the H-Maser
235
10
11.5 Automatic Cavity Tuning
245
2
11.6 The Wall Shift in Frequency
247
3
11.7 The H-Maser Signal Handling
250
3
11.8 Hydrogen as a Passive Resonator
253
2
Chapter 12. The Confinement of Ions
255
30
12.1 Introduction
255
1
12.2 State Selection in Ions
256
3
12.3 The Penning Trap
259
8
12.4 The Paul High-Frequency Trap
267
18
Chapter 13. The NASA Mercury Ion Experiment
285
22
13.1 Introduction
285
1
13.2 Ground State Hyperfine Structure of Hg^199
286
2
13.3 Hyperfine Optical Pumping
288
4
13.4 Detection of Microwave Resonance
292
1
13.5 Microwave Resonance Line Shape
293
3
13.6 The Magnetic Field Correction
296
1
13.7 The Physical Apparatus
297
4
13.8 Hg^+ Ion Frequency Standard System
301
6
Chapter 14. Optical Frequency Oscillators: Lasers
307
38
14.1 Introduction
307
1
14.2 The Resonance Line Width of Optical Cavities
307
5
14.3 Conditions for Sustained Oscillation
312
5
14.4 The Sustained Output Power
317
1
14.5 Laser Optical Elements
318
4
14.6 The Ruby Laser
322
5
14.7 The Helium-Neon Laser
327
5
14.8 The Argon Ion Laser
332
2
14.9 Liquid Dye Lasers
334
5
14.10 Semiconductor Lasers
339
6
Chapter 15. Laser Cooling of Atoms and Ions
345
24
15.1 Introduction
345
1
15.2 Light Pressure
346
2
15.3 Scattering of Light from Small Particles
348
2
15.4 Scattering of Light by Atoms
350
2
15.5 Optical Field Gradient Force
352
1
15.6 Doppler Cooling
353
3
15.7 Theoretical Limit
356
1
15.8 Optical "Molasses"
357
1
15.9 Polarization Gradient Cooling: "The Sisyphus Effect"
358
5
15.10 Laser Cooling of Trapped Ions
363
6
Chapter 16. Application of Lasers to Microwave Standards
369
26
16.1 Observation of Individual Ions
369
4
16.2 The Cooling Laser System
373
3
16.3 Laser Detection of Hyperfine Resonance
376
6
16.4 Laser-Based Mercury Ion Standards
382
1
16.5 The Proposed Ytterbium Ion Standard
383
1
16.6 Beating Liouville's Theorem
384
6
16.7 The Cesium Fountain Standard
390
5
Chapter 17. Measurement of Optical Frequency
395
24
17.1 Introduction
395
1
17.2 Definition of the Meter in Terms of the Second
396
1
17.3 Theoretical Limit to Spectral Purity of Lasers
396
3
17.4 Stabilization of Lasers Using Atomic/Molecular Resonances
399
1
17.5 Stabilization of the He-Ne Laser
400
6
17.6 Stabilization of the CO(2) Laser
406
1
17.7 Stabilization Using Two-Photon Transitions
407
2
17.8 Frequency Comparisons in the Optical Range
409
5
17.9 Measuring Optical Frequencies Relative to a Microwave Standard
414
5
Chapter 18. Applications: Time-Based Navigation
419
30
18.1 Introduction
419
1
18.2 "Deep" Space Probes
419
1
18.3 Very Long Baseline Interferometry
420
1
18.4 The Motion of the Earth
421
1
18.5 Radio Navigation
422
7
18.6 Navigation by Satellite
429
3
18.7 The Global Positioning System (GPS)
432
17
Chapter 19. Concluding Thoughts
449
8
19.1 The Synchronization of Clocks
449
2
19.2 The Direction of Time
451
2
19.3 Time-Reversal Symmetry in Subatomic Events
453
4
References
457
4
Further Reading
461
4
Index
465