Foreword ....................................................... xv
Preface ...................................................... xvii
Authors ....................................................... xix
1 Shedding light on the art of timekeeping ..................... 1
1.1 The great show of Time and Light, the curtain rises! .... 1
1.2 Brief history of timekeeping: time-frequency
equivalence ............................................. 2
1.3 The parallel story of the speed of light ................ 6
1.3.1 The laser arrives: length-frequency equivalence
and the birth of optical frequency metrology .... 14
1.3.2 Role of с in fundamental physics ................ 17
1.4 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 ........ 25
2.1 The ideal harmonic oscillator .......................... 25
2.1.1 Synchronization in coupled oscillators .......... 32
2.1.2 Beating two oscillators ......................... 35
2.2 Self-sustained oscillators ............................. 36
2.3 The noisy oscillator ................................... 41
2.4 Phase noise ............................................ 41
2.4.1 Review of mathematical tools .................... 42
2.4.2 Fundamental noise mechanisms .................... 44
2.4.2.1 Fluctuation-dissipation theorem (FDT) .. 48
2.5 Phase noise modelling .................................. 51
2.5.1 The Leeson effect ............................... 54
2.5.2 The Allan variance .............................. 57
2.5.3 Oscillator power spectrum in the carrier
frequency domain ................................ 62
2.5.3.1 Effect of frequency multiplication on
the power spectrum ..................... 65
2.6 Noise reduction in oscillators ......................... 66
2.6.1 Phase-locked loops .............................. 66
2.6.1.1 Optical phase-locked loops ............. 74
2.6.2 Injection locking ............................... 76
2.7 Phase noise measurements ............................... 80
2.7.1 Frequency counting .............................. 80
2.7.2 Homodyne techniques ............................. 81
2.7.3 Heterodyne techniques ........................... 82
2.7.4 Self-heterodyning ............................... 83
2.8 Amplitude noise measurements ........................... 84
2.8.1 AM noise in optical systems ..................... 85
3 Passive resonators .......................................... 87
3.1 Microwave cavities ..................................... 88
3.2 Basic properties of bulk optical cavities .............. 94
3.2.1 Fabry-Perot etalon .............................. 95
3.2.2 Paraxial ray analysis .......................... 101
3.2.3 Wave analysis .................................. 102
3.3 Cavity-design considerations .......................... 106
3.3.1 Quarter wave stack reflectors .................. 107
3.3.2 Prism-based cavities ........................... 111
3.4 Ultrastable cavities .................................. 117
3.4.1 Thermal stability .............................. 117
3.4.2 Vibration insensitive optical cavities ......... 123
3.5 Fiber cavities ........................................ 128
3.5.1 Directional coupler-based fiber cavities ....... 129
3.5.2 Resonators based on closely faced fiber tips ... 131
3.5.3 FBG-based fiber resonators ..................... 132
3.6 Whispering gallery mode resonators .................... 137
3.6.1 Wave theory of whispering gallery modes ........ 137
3.6.2 WGMs in a ray-optical picture .................. 150
3.6.3 Mode Q and volume .............................. 152
3.6.4 WGM evanescent coupling ........................ 154
3.6.5 Fabrication and applications of whispering
gallery resonators ............................. 159
4 Continuous-wave coherent radiation sources ................. 163
4.1 Principles of masers .................................. 164
4.1.1 The hydrogen maser ............................. 171
4.2 Compendium of laser theory ............................ 176
4.2.1 The active medium .............................. 177
4.2.1.1 Einstein A and В coefficients for
absorption and emission ............... 177
4.2.1.2 Line-broadening mechanisms ............ 180
4.2.2 The pump ....................................... 183
4.2.3 The resonator .................................. 186
4.2.4 Rate equations for a four-level system ......... 188
4.2.4.1 Transient behavior and relaxation
oscillation ........................... 191
4.3 Frequency pulling ..................................... 193
4.4 Achieving single-mode oscillation ..................... 194
4.4.1 Line selection ................................. 197
4.4.2 Single-tranverse mode selection ................ 198
4.4.3 Single-longitudinal mode selection ............. 198
4.5 The laser output ...................................... 202
4.5.1 Spatial coherence .............................. 202
4.5.2 Spectral and temporal coherence ................ 203
4.5.3 The effect of spontaneous emission ............. 205
4.5.3.1 Intrinsic laser linewidth ............. 206
4.5.3.2 Amplified spontaneous emission ........ 211
4.6 Laser frequency fluctuations and stabilization
techniques ............................................ 213
4.6.1 Side-lock to an atomic/molecular resonance ..... 219
4.6.2 Pound-Drever-Hall method ....................... 220
4.6.2.1 10-16-level laser frequency
stabilization ......................... 225
4.6.2.2 WGM resonators for laser frequency
stabilization ......................... 228
4.6.3 Hänsch-Couillaud technique ..................... 231
4.6.4 Laser frequency stabilization by locking to
an optical fiber-delay line .................... 233
4.6.5 Injection locking .............................. 237
4.7 Intensity fluctuations ................................ 240
4.7.1 High-sensitivity photodiode array .............. 243
4.7.2 Optical ac coupling ............................ 244
4.7.3 The laser as quasi-ideal oscillator ............ 246
4.8 Some specific laser systems ........................... 249
4.8.1 He-Ne laser .................................... 250
4.8.2 Carbon dioxide laser ........................... 251
4.8.3 Dye lasers ..................................... 253
4.8.4 Ion-doped lasers and optical amplifiers ........ 257
4.8.4.1 Nd:YAG laser .......................... 257
4.8.4.2 Ti:Sa laser ........................... 258
4.8.4.3 Erbium-doped fiber amplifiers
(EDFAs) ............................... 259
4.8.4.4 Ytterbium-doped fiber amplifiers
(YDFAs) ............................... 260
4.8.4.5 Narrow-linewidth fiber lasers ......... 263
4.8.5 Semiconductor lasers ........................... 268
4.8.5.1 Heterostructure diode lasers .......... 269
4.8.5.2 Distributed feedback (DFB) lasers ..... 285
4.8.5.3 Tapered semiconductor amplifiers ...... 288
4.8.5.4 Multiple-quantum-well lasers .......... 289
4.8.5.5 Vertical-cavity surface-emitting
lasers ................................ 292
4.8.5.6 Quantum cascade lasers ................ 292
4.8.5.7 Interband cascade lasers .............. 300
4.8.6 Nonlinear laser cw sources ..................... 302
4.8.6.1 Sum frequency generation .............. 305
4.8.6.2 Optical parametric oscillators ........ 306
4.8.6.3 Difference frequency generators ....... 312
4.8.6.4 Tunable far-infrared radiation ........ 317
5 High-resolution spectroscopic frequency measurements ....... 323
5.1 Interferometric wavelength measurements ............... 323
5.2 Spectroscopic frequency measurements .................. 328
5.2.1 Principles of absorption laser spectroscopy .... 329
5.3 Frequency modulation spectroscopy ..................... 329
5.3.1 Harmonic detection ............................. 330
5.3.2 Wavelength modulation spectroscopy ............. 331
5.3.3 Single- and two-tone frequency modulation
spectroscopy ................................... 331
5.4 Magnetic rotation spectroscopy ........................ 337
5.5 Cavity-enhanced spectroscopy .......................... 341
5.5.1 Cavity-enhanced absorption spectroscopy ........ 342
5.5.2 Off-axis integrated cavity output
spectroscopy ................................... 343
5.5.3 Noise immune cavity-enhanced optical
heterodyne molecular spectroscopy .............. 346
5.5.4 Cavity ring-down spectroscopy .................. 348
5.5.4.1 Phase-shift (PS) CRDS ................. 350
5.5.4.2 Saturated-absorption cavity
ring-down spectroscopy ................ 351
5.6 Doppler-free saturation spectroscopy .................. 354
5.6.1 Frequency locking to a Lamb dip ................ 358
5.6.2 Cavity-enhanced Doppler-free saturation
spectroscopy ................................... 361
5.6.2.1 Doppler-free NICE-OHMS ................ 363
5.7 Doppler-free polarization spectroscopy ................ 364
5.8 Doppler-free two-photon spectroscopy .................. 368
5.9 Second-order Doppler-free spectroscopy ................ 372
5.10 Sub-Doppler spectroscopy in atomic/molecular beams .... 374
5.10.1 Effusive beams ................................. 374
5.10.2 Supersonic beams ............................... 377
5.10.3 Buffer-gas-cooling ............................. 379
5.11 Ramsey fringes ........................................ 381
5.12 Laser frequency standards using thermal quantum
absorbers ............................................. 387
5.12.1 Iodine-stabilized lasers ....................... 388
5.12.2 Acetylene-stabilized lasers .................... 388
5.12.3 Methane-stabilized lasers ...................... 389
5.12.4 OsO4-stabilized lasers ......................... 389
5.12.5 Atomic hydrogen standard ....................... 390
5.12.6 Calcium standard ............................... 393
5.13 Fourier transform spectroscopy ........................ 394
5.14 Raman spectroscopy .................................... 398
5.14.1 Coherent anti-Stokes spectroscopy .............. 405
5.14.2 Stimulated Raman scattering .................... 410
6 Time and frequency measurements with pulsed laser systems .. 413
6.1 Introduction .......................................... 413
6.2 Theory of mode locking ................................ 415
6.3 Mode-locking mechanisms and dispersion compensation
schemes ............................................... 417
6.3.1 Ti:sapphire lasers and Kerr-lens mode locking .. 417
6.3.2 Fiber-based lasers and nonlinear-
polarization-rotation mode-locking ............. 419
6.4 Optical frequency comb synthesis from mode-locked
lasers ................................................ 421
6.4.1 Comb stabilization ............................. 421
6.4.2 Measurements with a frequency comb ............. 425
6.4.2.1 Measuring frequency differences ....... 425
6.4.2.2 Measuring absolute frequencies with
an octave-spanning comb ............... 426
6.4.2.3 Absolute optical frequency
synthesizer ........................... 427
6.4.2.4 Direct frequency-comb spectroscopy .... 429
6.4.2.5 Other measurement schemes and
applications .......................... 435
6.4.3 Relevant properties of a mode-locked laser
for frequency-comb applications ................ 440
6.4.4 Microresonator-based frequency combs ........... 441
6.5 Extension of OFCSs into novel spectral regions ........ 444
6.5.1 High-order laser harmonics and extensions to
the XUV ........................................ 444
6.5.1.1 Generation and properties of
high-order laser harmonics ............ 446
6.5.1.2 Ramsey-type spectroscopy in the XUV
with high-order harmonics ............. 448
6.5.1.3 Cavity-enhanced XUV frequency combs ... 456
6.5.1.4 Attosecond pulses ..................... 459
6.5.2 Mid- and far-infrared OFCSs .................... 460
7 Frequency standards ........................................ 465
7.1 General features of frequency standards and clocks .... 465
7.2 Quartz oscillators .................................... 466
7.2.1 Factors affecting crystal oscillator
frequency accuracy ............................. 471
7.2.2 Factors affecting frequency stability .......... 473
7.2.3 State-of-the-art ultrastable quartz
oscillators .................................... 473
7.3 Cryogenic sapphire oscillators ........................ 473
7.4 Photonic microwave oscillators based on WGM
resonators ............................................ 479
7.5 Generation of ultrastable microwaves via optical
frequency division .................................... 480
7.6 Trapping and cooling of neutral atoms ................. 482
7.6.1 Optical molasses ............................... 483
7.6.2 Magneto-optical traps .......................... 489
7.6.3 Bose-Einstein condensation ..................... 492
7.6.3.1 Magnetic trapping ..................... 492
7.6.3.2 Evaporative cooling ................... 493
7.6.3.3 Probing а ВЕС ......................... 495
7.7 Cold stable molecules ................................. 498
7.7.1 Stark decelerator .............................. 498
7.8 Trapping and cooling of ions .......................... 500
7.8.1 Paul traps ..................................... 500
7.8.1.1 Linear Paul traps ..................... 504
7.8.2 Penning traps .................................. 505
7.8.3 Trap loading ................................... 507
7.8.4 Ion cooling techniques ......................... 507
7.8.4.1 Laser cooling ......................... 508
7.8.4.2 Sympathetic cooling ................... 511
7.8.5 Spectroscopy of trapped particles in the
Lamb-Dicke regime .............................. 511
7.9 Microwave atomic standards ............................ 513
7.9.1 Metrological properties of the active
hydrogen maser ................................. 513
7.9.1.1 Maser design .......................... 513
7.9.1.2 Frequency shifts ...................... 513
7.9.1.3 Automatic tuning of the resonant
cavity ................................ 515
7.9.1.4 Frequency stability ................... 516
7.9.1.5 Cryogenic hydrogen masers ............. 517
7.9.2 Cesium clocks .................................. 518
7.9.2.1 Cesium-beam frequency standards ....... 518
7.9.2.2 Cesium fountain clocks ................ 521
7.9.2.3 Uncertainty budget in a Cs fountain
clock ................................. 527
7.9.3 Rubidium clocks ................................ 532
7.9.3.1 Rb fountain clocks .................... 533
7.9.3.2 Lamp-based Rb cell standards .......... 534
7.9.3.3 Laser-based Rb cell frequency
standards ............................. 535
7.9.4 Microwave ion clocks ........................... 539
7.10 Time transfer and frequency dissemination ............. 541
7.10.1 Realization of time scales ..................... 542
7.10.1.1 Realization of TAI .................... 542
7.10.1.2 Coordinated universal time ............ 543
7.10.2 Transmitting time information .................. 543
7.10.2.1 Portable clocks ....................... 546
7.10.2.2 Global positioning system ............. 547
7.10.3 Frequency transfer ............................. 550
7.10.3.1 A democratic absolute frequency
chain ................................. 550
7.10.3.2 Dissemination of microwave frequency
standards ............................. 551
7.10.3.3 Optical frequency transfer ............ 552
8 Future trends in fundamental physics and applications ...... 557
8.1 Optical atomic clocks ................................. 557
8.1.1 Trapped ion optical clocks ..................... 559
8.1.1.1 Systematic frequency shifts ........... 562
8.1.2 Neutral atoms optical lattice clocks ........... 564
8.2 The hydrogen atom as an inexhaustible wellspring of
advances in precision spectroscopy .................... 570
8.2.1 Determination of the Rydberg constant and of
the proton radius .............................. 572
8.3 Spectroscopy of cold, trapped metastable helium ....... 575
8.4 Measurements of fundamental constants ................. 578
8.4.1 Boltzmann constant кв .......................... 578
8.4.2 Newton gravitational constant G ................ 580
8.5 Constancy of fundamental constants .................... 582
8.5.1 Fine structure constant a ...................... 584
8.5.1.1 Proton-to-electron mass ratio 0 ....... 586
8.5.2 Speed of light с ............................... 588
8.5.2.1 Frequency dependence of с and the
mass of the photon .................... 588
8.5.3 Newton's gravitational constant ................ 590
8.6 Tests of fundamental physics laws ..................... 590
8.6.1 Spectroscopic tests of spin-statistic
connection and symmetrization postulate ........ 590
8.6.2 Search for the electron dipole moment .......... 594
8.6.3 Parity violation in chiral molecules ........... 595
8.7 Perspectives for precision spectroscopy of cold
molecules ............................................. 600
8.8 Tests of general relativity: from ground-based
experiments to space missions ......................... 603
8.8.1 Testing the Einstein Equivalence Principle ..... 604
8.8.1.1 Tests of UFF .......................... 604
8.8.1.2 Tests of LLI .......................... 605
8.8.1.3 Tests of LPI .......................... 608
8.8.2 Test of post-Newtonian gravity ................. 610
8.8.3 Tests of the gravitational inverse square law .. 611
8.8.3.1 Detection of gravitational waves ...... 611
8.9 Quantum-enhanced time and frequency measurements ...... 613
8.9.1 Standard quantum limit in physical
measurements ................................... 613
8.9.2 Using nonclassical light states for quantum-
enhanced measurements .......................... 615
8.9.3 Applications to time and frequency
measurements ................................... 620
8.9.3.1 Quantum logic spectroscopy ............ 620
8.9.3.2 Time and frequency quantum metrology .. 621
8.9.3.3 Quantum positioning and clock
synchronization ....................... 623
8.10 Environmental metrology ............................... 625
8.10.1 Geophysical survey of volcanic areas ........... 625
8.10.2 Detection of very rare isotopes ................ 628
8.10.3 Stratospheric survey with tunable diode laser
spectrometers .................................. 628
8.10.4 Fiber sensing of physical and chemical
parameters ..................................... 630
8.10.4.1 Strain sensing ........................ 632
8.10.4.2 Acceleration measurements ............. 633
8.10.4.3 Chemical sensing by optical-fiber
ring resonators ....................... 634
Bibliography ............................................... 637
Index ......................................................... 701
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