Laser-Based Measurements for Time and Frequency

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1 Laser-Based Measurements for Time and Frequency Domain Applications A Handbook Pasquale Maddaloni Marco Bellini Paolo De Natale CRC Press Taylor Si Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TAYLOR & FRANCIS BOOK

2 Contents Foreword Preface Authors xv xvii xix 1 Shedding light on the art of timekeeping The great show of Time and Light, the curtain rises! Brief history of timekeeping: time-frequency equivalence The parallel story of the speed of light The laser arrives: length-frequency equivalence and the birth of optical frequency metrology Role of c in fundamental physics In the end, time and light met up again: optical atomic clocks and outline of the book 20 2 Characterization and control of harmonic oscillators The ideal harmonic oscillator Synchronization in coupled oscillators Beating two oscillators Self-sustained oscillators The noisy oscillator Phase noise Review of mathematical tools Fundamental noise mechanisms Fluctuation-dissipation theorem (FDT) Phase noise modelling The Leeson effect The Allan variance Oscillator power spectrum in the carrier frequency domain Effect of frequency multiplication on the power spectrum 2.6 Noise reduction in oscillators Phase-locked loops ,1 Optical phase-locked loops Injection locking Phase noise measurements Frequency counting Homodyne techniques Heterodyne techniques Self-heterodyning 83 vii

3 viii Contents 2.8 Amplitude noise measurements AM noise in optical systems 85 3 Passive resonators Microwave cavities Basic properties of bulk optical cavities Fabry-Perot etalon Paraxial ray analysis Wave analysis Cavity-design considerations Quarter wave stack reflectors Prism-based cavities Ill 3.4 Ultrastable cavities Thermal stability Vibration insensitive optical cavities Fiber cavities Directional coupler-based fiber cavities Resonators based on closely faced fiber tips FBG-based fiber resonators Whispering gallery mode resonators Wave theory of whispering gallery modes WGMs in a ray-optical picture Mode Q and volume WGM evanescent coupling Fabrication and applications of whispering gallery resonators Continuous-wave coherent radiation sources Principles of masers The hydrogen maser Compendium of laser theory The active medium Einstein A and B coefficients for absorption and emission Line-broadening mechanisms The pump The resonator Rate equations for a four-level system Transient behavior and relaxation oscillation Frequency pulling Achieving single-mode oscillation Line selection Single-tranverse mode selection Single-longitudinal mode selection The laser output Spatial coherence Spectral and temporal coherence The effect of spontaneous emission Intrinsic laser linewidth Amplified spontaneous emission Laser frequency fluctuations and stabilization techniques 213

4 Contents ix Side-lock to an atomic/molecular resonance Pound-Drever-Hall method ~~16-level laser frequency stabilization WGM resonators for laser frequency stabilization Hansch-Couillaud technique Laser frequency stabilization by locking to an optical fiber-delay line Injection locking Intensity fluctuations High-sensitivity photodiode array Optical ac coupling The laser as quasi-ideal oscillator Some specific laser systems He-Ne laser Carbon dioxide laser Dye lasers Ion-doped lasers and optical amplifiers Nd:YAG laser Ti:Sa laser Erbium-doped fiber amplifiers (EDFAs) Ytterbium-doped fiber amplifiers (YDEAs) Narrow-linewidth fiber lasers Semiconductor lasers Heterostructure diode lasers Distributed feedback (DFB) lasers Tapered semiconductor amplifiers Multiple-quantum-well lasers Vertical-cavity surface-emitting lasers Quantum cascade lasers Interband cascade lasers Nonlinear laser cw sources Sum frequency generation Optical parametric oscillators Difference frequency generators Tunable far-infrared radiation High-resolution spectroscopic frequency measurements Interferometric wavelength measurements Spectroscopic frequency measurements Principles of absorption laser spectroscopy Frequency modulation spectroscopy Harmonic detection Wavelength modulation spectroscopy Single- and two-tone frequency modulation spectroscopy Magnetic rotation spectroscopy Cavity-enhanced spectroscopy Cavity-enhanced absorption spectroscopy Off-axis integrated cavity output spectroscopy Noise immune cavity-enhanced optical heterodyne molecular spectroscopy Cavity ring-down spectroscopy 348

5 X Contents Phase-shift (PS) CRDS Saturated-absorption cavity ring-down spectroscopy Doppler-free saturation spectroscopy Frequency locking to a Lamb dip Cavity-enhanced Doppler-free saturation spectroscopy Doppler-free NICE-OHMS Doppler-free polarization spectroscopy Doppler-free two-photon spectroscopy Second-order Doppler-free spectroscopy Sub-Doppler spectroscopy in atomic/molecular beams Effusive beams Supersonic beams Buffer-gas-cooling Ramsey fringes Laser frequency standards using thermal quantum absorbers Iodine-stabilized lasers Acetylene-stabilized lasers Methane-stabilized lasers Os04-stabilized lasers Atomic hydrogen standard Calcium standard Fourier transform spectroscopy Raman spectroscopy Coherent anti-stokes spectroscopy Stimulated Raman scattering Time and frequency measurements with pulsed laser systems Introduction Theory of mode locking Mode-locking mechanisms and dispersion compensation schemes 417 harmonics Tksapphire lasers and Kerr-lens mode locking Fiber-based lasers and nonlinear-polarization-rotation mode-locking Optical frequency comb synthesis from mode-locked lasers Comb stabilization Measurements with a frequency comb Measuring frequency differences Measuring absolute frequencies with an octave-spanning comb Absolute optical frequency synthesizer Direct frequency-comb spectroscopy Other measurement schemes and applications Relevant properties of a mode-locked laser for frequency-comb applications Microresonator-based frequency combs Extension of OFCSs into novel spectral regions High-order laser harmonics and extensions to the XUV Generation and properties of high-order laser Ramsey-type spectroscopy in the XUV with high-order harmonics Cavity-enhanced XUV frequency combs 456

6 Contents xi Attosecond pulses Mid-and far-infrared OFCSs Frequency standards General features of frequency standards and clocks Quartz oscillators Factors affecting crystal oscillator frequency accuracy Factors affecting frequency stability State-of-the-art ultrastable quartz oscillators Cryogenic sapphire oscillators Photonic microwave oscillators based on WGM resonators Generation of ultrastable microwaves via optical frequency division Trapping and cooling of neutral atoms Optical molasses Magneto-optical traps Bose-Einstein condensation Magnetic trapping Evaporative cooling Probing a BEC Cold stable molecules Stark decelerator Trapping and cooling of ions Paul traps Linear Paul traps Penning traps Trap loading Ion cooling techniques Laser cooling Sympathetic cooling Spectroscopy of trapped particles in the Lamb-Dicke regime Microwave atomic standards Metrological properties of the active hydrogen maser Maser design Frequency shifts Automatic tuning of the resonant cavity Frequency stability Cryogenic hydrogen masers Cesium clocks Cesium-beam frequency standards Cesium fountain clocks Uncertainty budget in a Cs fountain clock Rubidium clocks Rb fountain clocks Lamp-based Rb cell standards Laser-based Rb cell frequency standards Microwave ion clocks Time transfer and frequency dissemination Realization of time scales Realization of TAI 542

7 xii Contents Coordinated universal time Transmitting time information Portable clocks Giobal positioning system Frequency transfer A democratic absolute frequency chain Dissemination of microwave frequency standards Optical frequency transfer Future trends in fundamental physics and applications Optical atomic clocks Trapped ion optical clocks Systematic frequency shifts Neutral atoms optical lattice clocks The hydrogen atom as an inexhaustible wellspring of advances in precision spectroscopy Determination of the Rydberg constant and of the proton radius. 8.3 Spectroscopy of cold, trapped metastable helium Measurements of fundamental constants Boltzmann constant Ub Newton gravitational constant G Constancy of fundamental constants Fine structure constant a Proton-to-electron mass ratio / Speed of light c Frequency dependence of c and the mass of the photon Newton's gravitational constant Tests of fundamental physics laws Spectroscopic tests of spin-statistic connection and symmetrization postulate Search for the electron dipole moment Parity violation in chiral molecules Perspectives for precision spectroscopy of cold molecules Tests of general relativity: from ground-based experiments to space missions Testing the Einstein Equivalence Principle Tests of UFF Tests of LLI Tests of LPI Test of post-newtonian gravity Tests of the gravitational inverse square law Detection of gravitational waves Quantum-enhanced time and frequency measurements Standard quantum limit in physical measurements Using nonclassical light states for quantum-enhanced measurements Applications to time and frequency measurements Quantum logic spectroscopy Time and frequency quantum metrology Quantum positioning and clock synchronization Environmental metrology 625

8 Contents xiii Geophysical survey of volcanic areas Detection of very rare isotopes Stratospheric survey with tunable diode laser spectrometers Fiber sensing of physical and chemical parameters Strain sensing Acceleration measurements Chemical sensing by optical-fiber ring resonators 634 Bibliography 637 Index 701

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