The Quantum Beat. Second Edition

Transcription

1 The Quantum Beat Second Edition

2 F.G. Major The Quantum Beat Principles and Applications of Atomic Clocks Second Edition

3 F.G. Major 284 Michener Court E. Severna Park, MD USA Figure 1.4 Courtesy of the British Museum, London. Figure 8.8 Courtesy of Tekelec Neuchâtel Time, S.A. Avenue du Mail 59, CH 2000 Neuchâtel, Switzerland. Figure 19.4 Courtesy of NASA-Headquarters, Still Photograph Library, Washington, D.C. Drawings by Monica Williams, Annapolis, and Christopher Major, New York, Library of Congress Control Number: ISBN ISBN (ebook) c 2007, 1998 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com

4 Preface Since the publication of the first edition of this book in 1998, the realm of optical frequency measurement has opened up with the development of extremely broad band frequency combs extending over a full octave on the frequency scale. This has enabled the direct coherent calibration of the frequency of an optical clock with respect to the microwave Cs standard. This continues at an accelerating pace the revolutionary changes that the field of frequency and time measurement has undergone in recent years, with regard both to its precision and particularly to its extension to include optical frequencies. What began as the introduction of techniques to cool atoms and ions through interaction with suitable laser beams, coupled with methods of particle suspension in ultra-high vacuum, has been carried forward to an astonishing degree with ultrasharp resonances being observed at optical frequencies on individual ions stored in ultrahigh vacuum for extended periods of time. This brings us to the point of the ideal first expressed by Dehmelt of making observations on isolated atomic particles at rest in space. This was the author s own motivating principle in the initial experiments on a field-confined mercury ion standard for space applications. The rapid progress in the stabilization and synthesis of optical frequency signals using solid-state sources has brought about unprecedented degrees of long and short term stability, with the prospect of developing a new generation of space-hardened optical clocks. The implementation of a satellite global navigation system, the Global Positioning System (GPS), is the most visible example of the enormous impact that atomic frequency standards have had on the civilian and the military sectors of society. The crucial elements in this system are the spacecraft atomic clocks, without which it could not exist. It has become very much part of our culture permeating many aspects of our life and technology. The cesium and rubidium clocks aboard the satellites maintain submicrosecond synchronization, putting the accuracy of position determination globally in the submeter range! As with the first edition, the object is to convey a broad understanding of the physical principles underlying the workings of these quantum-based atomic clocks, with introductory chapters placing them in context with the early development of

5 vi Preface mechanical clocks and the introduction of electronic time-keeping as embodied in the quartz-controlled clocks. While the book makes no pretense at being a history of atomic clocks, it nevertheless takes a historical perspective in its treatment of the subject. Intended for non-specialists with some knowledge of physics or engineering, The Quantum Beat covers a wide range of salient topics relevant to atomic clocks, treated in a broad intuitive manner with a minimum of mathematical formalism. Detailed descriptions are given of the design principles of the rubidium, cesium, hydrogen maser, and mercury ion standards; the revolutionary changes that the advent of the laser has made possible, such as laser cooling, optical pumping, the formation of optical molasses, the cesium fountain standard, as well as topics that bear on the precision and absolute accuracy of standards, such as noise, resonance line shape, and the relativistic Doppler effect. Also included are the timebased global navigation systems: Loran-C and the Global Positioning System, as well as tests of invariance principles and symmetry in fundamental unified theory, such as the constancy of physical constants such as the fine structure constant in atomic physics, and tests of Einstein s Equivalence Principle. I am greatly indebted to the following for the encouragement I derived from their willingness to read and provide valuable suggestions on parts of the manuscript: Professors Norman Ramsey, Claude Cohen-Tannoudji, Gisbert zu Putlitz, Charles Drake, Hugh Robinson, and especially my friends and former colleagues Professor Herbert Ueberall, and Claude Audoin of BNM/LPTF Observatoire de Paris. Severna Park, Maryland, USA September 4, 2006 F.G. Major

6 Contents Chapter 1. Celestial and Mechanical Clocks CyclicEventsinNature The Calendar SolarEclipsesasTimeMarkers TheTides TheSiderealDay ThePrecessionoftheEquinoxes The Sundial TheAstrolabe Water Clocks Tower Clocks The Pendulum Clock The Spring Balance-Wheel Clock Chapter 2. Oscillations and Fourier Analysis Oscillatory Motion in Matter SimpleHarmonicMotion Forced Oscillations: Resonance Waves in Extended Media WaveDispersion Linear and Nonlinear Media Normal Modes of Vibration ParametricExcitations FourierAnalysis Coupled Oscillations Chapter 3. Oscillators Feedback in Amplifiers Conditions for Oscillation... 48

7 viii Contents 3.3 Resonators TheKlystronMicrowaveTube Oscillators at Optical Frequency Stability of Oscillators Chapter 4. Quartz Clocks Historical Antecedents Properties and Structure of Crystalline Quartz Modes of Vibration of a Quartz Plate X-RayCrystallography Fabrication of Quartz Resonators Stability of Resonance Frequency The Quartz Resonator as a Circuit Element Frequency/Time Measurement 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 Schrödinger Wave Equation Quantum Numbers of Atomic States The Vector Model The Shell Structure of Electron States ThePauliExclusionPrinciple Spectroscopic Notation The Hyperfine Interaction Electrons in Solids: The Band Theory Chapter 6. Magnetic Resonance Introduction Atomic Magnetism TheZeemanEffect Gyroscopic Motion in a Magnetic Field Inducing Transitions Motion of Global Moment: The Bloch Theory Production of Global Polarization Chapter 7. Corrections to Observed Atomic Resonance Resonance Frequency Broadening Thermal Doppler Broadening RelativisticEffects Conclusion

8 Contents ix Chapter 8. The Rubidium Clock The Reference Hyperfine Transition TheBreit RabiFormula Optical Pumping of Hyperfine Populations Optical Hyperfine Pumping: Use of an Isotopic Filter TheUseofBufferGases Light Shifts in the Reference Frequency Rubidium Frequency Control of Quartz Oscillator Frequency Stability of the Rubidium Standard The Miniaturization of Atomic Clocks Chapter 9. The Classical Cesium Standard Definition of the Unit of Time Implementation of the Definition: The Cesium Standard ThePhysicalDesign DetectionofTransitions Frequency-Lock of Flywheel Oscillator to Cesium Corrections to the Observed Cs Frequency Chapter 10. Atomic and Molecular Oscillators: Masers TheAmmoniaMaser BasicElementsofaBeamMaser Inversion Spectrum in NH TheElectrostaticStateSelector StimulatedRadiationintheCavity Threshold for Sustained Oscillation Sources of Frequency Instability TheRubidiumMaser Chapter 11. The Hydrogen Maser Introduction The Hyperfine Structure of H Ground State Principles of the Hydrogen Maser PhysicalDesignoftheH-Maser AutomaticCavityTuning The Wall Shift in Frequency The H-Maser Signal Handling Chapter 12. The Confinement of Particles in Fields Introduction The Penning Trap The Paul High-Frequency Trap FieldDistortionduetoIons

9 x Contents 12.5 The Effect of Collisions IonObservation Laser Resonance Fluorescence Detection Chapter 13. Isolated Ion Clock: A New Approach The Original Concept Hyperfine Resonance in Trapped 199 Hg + Ions A Portable Hg 199 Ion Microwave Standard Chapter 14. Optical Frequency Oscillators: Lasers Fundamentals Laser Beam Properties LaserOpticalElements Chapter 15. Laser Systems TheGasLasers LiquidDyeLasers Semiconductor Lasers Solid Crystalline Lasers Chapter 16. Laser Cooling of Atoms and Ions Introduction LightPressure ScatteringofLightfromSmallParticles ScatteringofLightbyAtoms OpticalFieldGradientForce Doppler Cooling Theoretical Limit Optical Molasses and the Magneto-Optical Trap Polarization Gradient Cooling: The Sisyphus Effect Laser Cooling of Trapped Ions Chapter 17. Application of Lasers to Microwave Standards Observation of Individual Ions Optical Detection of Hyperfine Transitions The NIST Mercury Ion Microwave Standard The Proposed Ytterbium Ion Standard The Laser Pumped Cesium Beam Standard The Cesium Fountain Standard

10 Contents xi Chapter 18. Optical Standards and Measurement Introduction Definition of the Meter in Terms of the Second Secondary Optical Frequency Standards Optical Standards Based on Laser Cooled Ions Optical Frequency Chains Optical Frequency Comb Generators Chapter 19. Applications: Time-Based Navigation Introduction Deep Space Probes VeryLongBaselineInterferometry TheMotionoftheEarth RadioNavigation Navigation by Satellite The Global Positioning System (GPS) Chapter 20. Atomic Clocks and Fundamental Physics Introduction Einstein s Equivalence Principle (EEP) LorentzSymmetry Symmetry in Fundamental Physics TheCPTSymmetry The String Theory Experiments on ISS (International Space Station) Conclusion References 461 Further Reading 467 Index 471