F.G. Major. The Quantum Beat. The Physical Principles of Atomic Clocks. With 230 Illustrations. Springer

Transcription

1 F.G. Major The Quantum Beat The Physical Principles of Atomic Clocks With 230 Illustrations Springer

2 Contents Preface Chapter 1. Celestial and Mechanical Clocks Cyclic Events in Nature The Calendar Solar Eclipses as Time Markers The Tides The Sidereal Day The Precession of the Equinoxes The Sundial The Astrolabe Water Clocks Tower Clocks The Pendulum Clock The Spring-Balance-Wheel Clock 19 Chapter 2. Oscillations and Fourier Analysis Oscillatory Motion in Matter Simple Harmonic Motion Forced Oscillations: Resonance Waves in Extended Media Wave Dispersion ' Linear and Nonlinear Media Normal Modes of Vibration Parametric Excitations Fourier Analysis Coupled Oscillations 43 Chapter 3. Oscillators Feedback in Amplifiers Conditions for Oscillation 50 vii

3 x Contents 3.3 Resonators The Klystron Microwave Tube Oscillators at Optical Frequency Stability of Oscillators: Noise 58 Chapter 4. Quartz Clocks Historical Antecedents Properties and Structure of Crystalline Quartz Modes of Vibration of a Quartz Plate X-Ray Crystallography Fabrication of Quartz Resonators Factors Affecting the Resonance Frequency The Quartz Resonator as a Circuit Element Frequency Stability Frequency/Time Measurement Quartz Watches 88 Chapter 5. The Language of Electrons, Atoms, and Quanta Classical Lorentz Theory Spectrum of Blackbody Radiation The Quantum of Radiation: The Photon Bohr's Theory of the Hydrogen Atom The SchrSdinger Wave Equation Quantum Numbers of Atomic States The Vector Model The Shell Structure of Electron States The Pauli Exclusion Principle Spectroscopic Notation The Hyperfine Interaction Electrons in Solids: The Band Theory 109 Chapter 6. Magnetic Resonance Introduction Atomic Magnetism The Zeeman Effect Gyroscopic Motion in a Magnetic Field Inducing Transitions Motion of Global Moment: The Bloch Theory 127

4 Contents xi 6.7 Production of Global Polarization 128 Chapter 7. Corrections to Observed Atomic Resonance Homogeneous and Inhomogeneous Broadening The Special Theory of Relativity The Doppler Effect The Thermal Doppler Line Shape Sub-Doppler Line Widths: the Dicke Effect The General Theory of Relativity Conclusion 159 Chapter 8. The Rubidium Clock The Reference Hyperfine Transition The Breit-Rabi Formula Optical Pumping of Hyperfine Populations Optical Hyperfine Pumping: Use of an Isotopic Filter The Use of Buffer Gases Light Shifts in the Reference Frequency Rubidium Frequency Control of Quartz Oscillator Frequency Stability of the Rubidium Standard The Miniaturization of Atomic Clocks 178 Chapter 9. The Classical Cesium Standard Definition of the Unit of Time Implementation of the Definition: The Cesium Standard The Physical Design The Ramsey Separated Field Detection of Transitions Frequency-Lock of Flywheel Oscillator to Cesium Corrections to the Observed Cs Frequency 201 Chapter 10. Atomic and Molecular Oscillators: Masers The Ammonia Maser Basic Elements of a Beam Maser Inversion Spectrum in NH The Electrostatic State Selector Stimulated Radiation in the Cavity Threshold for Sustained Oscillation 216

5 xii Contents 10.7 Sources of Frequency Instability The Rubidium Maser 221 Chapter 11. The Hydrogen Maser Introduction The Hyperfine Structure of H Ground State Principles of the Hydrogen Maser Physical Design of the H-Maser Automatic Cavity Tuning The Wall Shift in Frequency The H-Maser Signal Handling Hydrogen as apassive Resonator 253 Chapter 12. The Confinement of Ions Introduction State Selection in Ions The Penning Trap The Paul High-Frequency Trap 267 Chapter 13. The NASA*Mercury Ion Experiment Introduction Ground State Hyperfine Structure of Hg 1 " Hyperfine Optical Pumping Detection of Microwave Resonance Microwave Resonance Line Shape The Magnetic Field Correction The Physical Apparatus ; Hg + Ion Frequency Standard System 301 Chapter 14. Optical Frequency Oscillators: Lasers Introduction The Resonance Line Width of Optical Cavities Conditions for Sustained Oscillation The Sustained Output Power Laser Optical Elements The Ruby Laser The Helium-Neon Laser The Argon Ion Laser 332

6 Contents xiii 14.9 Liquid Dye Lasers : Semiconductor Lasers 339 Chapter 15. Laser Cooling of Atoms and Ions Introduction Light Pressure Scattering of Light from Small Particles Scattering of Light by Atoms Optical Field Gradient Force Doppler Cooling Theoretical Limit Optical "Molasses" Polarization Gradient Cooling: "The Sisyphus Effect" Laser Cooling of Trapped Ions 363 Chapter 16. Application of Lasers to Microwave Standards Observation of Individual Ions The Cooling Laser System Laser Detection of Hyperfine Resonance Laser-Based Mercury Ion Standards The Proposed Ytterbium Ion Standard Beating Liouville's Theorem The Cesium Fountain Standard 390 Chapter 17. Measurement of Optical Frequency Introduction Definition of the Meter in Terms of the Second Theoretical Limit to Spectral Purity of Lasers Stabilization of Lasers Using Atomic/Molecular Resonances Stabilization of the He-Ne Laser Stabilization of the CO 2 Laser Stabilization Using Two-Photon Transitions Frequency Comparisons in the Optical Range Measuring Optical Frequencies Relative to a Microwave Standard 414 Chapter 18. Applications: Time-Based Navigation Introduction 419

7 xiv Contents 18.2 "Deep" Space Probes Very Long Baseline Interferometry The Motion of the Earth Radio Navigation Navigation by Satellite The Global Positioning System (GPS) 432 Chapter 19. Concluding Thoughts The Synchronization of Clocks The Direction of Time Time-Reversal Symmetry in Subatomic Events 453 References 457 Further Reading 461 Index 465