Index#

3j symbol, 93, 956j symbol, 94, 95

Abraham force, 46, 52 Abraham momentum density, 40, 46, 51 Abraham photon momentum, 452 Abraham–Lorentz equation, 372, 375, 376, 378 absorption as destructive interference efect, 271–273 cross section, 108 amplification, 379 noise, 379 amplified spontaneous emission, 388, 390, 397–401 anomalous dispersion, 105 anti-normal order, 174, 179, 181, 388, 396, 519 argument theorem, 420, 453, 454, 464, 511 atomic cascade transition, 301, 304, 305, 309 attenuation coeficient, 55, 59, 61–64, 66, 67 Rayleigh scattering, 55, 59, 61–64 Thomson scattering, 66, 67

Baker–Hausdorf theorem, 150 bare mass, 221, 375, 378 beam splitter, 402–406 input–output relations, 402, 404 Bell state, 311, 312 Bell’s theorem, 316–319 experiments, 319–321 blackbody radiation, 81, 92, 112–114, 117–121, 123, 162, 181, 325, 338, 351, 376, 377 fluctuations and dissipation, 121 level shifts, 91, 92 Lorentz transformation, 117 Bloch equations, 69, 106–108, 110, 269–271, 273, 294, 299, 502 rate equations, 109, 110 Bloch sphere, 106, 107 Bloch vector, 106 Bloch–Siegert shift, 104, 287 blue sky, 55, 60 Bohr–Kramers–Slater theory, 193, 194 Bose–Einstein distribution, 121, 159, 165, 174, 392, 396, 397, 399 generating function, 174 variance, 392 Bose–Einstein statistics, 119, 163

Bothe–Geiger experiment, 194 Brownian motion, 121, 147, 325–328, 330, 333, 335, 337–339, 341, 357 ballistic regime, 335 difusive regime, 33 Casimir force, 401, 425, 426, 428–431 conducting spherical shell, 431 zero-point energy, 425, 428 zero-point field pressure, 428 Casimir–Polder interaction, 416, 417, 419, 431–434, 446 Cauchy dispersion formula, 27 causality, 310, 361, 362, 371, 412, 511, 516, 519 cavity perturbation theory, 435, 437, 438 center-of-gravity theorem, 43 central limit theorem, 164, 385 chaotic radiation, 123, 168, 181 characteristic function, 172, 173, 338 classical electron radius, 66, 372 Clausius–Mossotti relation, 54, 430 clock-in-a-box experiment, 195 cloning fidelity, 310 coherent states, 148–156, 159, 160, 162, 166, 175, 176, 270, 271, 278, 279, 282, 290, 291, 297 equivalent definitions, 149 minimal uncertainty product, 148, 198 overcompleteness, 152 produced by classically prescribed source, 153–155 collapses and revivals, 282, 283 completeness theorem for Hermitian operators, 70, 132 Compton scattering, 66 concurrence, 312 Coulomb gauge, 7, 13, 14, 133, 141, 207–209, 211, 497, 513, 514 retarded electric field, 14, 209, 214, 513, 514 Coulomb self-energy, 208, 255 coupling constant integration algorithm, 422 Debye induction interaction, 410 delayed choice, 321 density fluctuations, 56, 57 density matrix, 85, 171, 172, 180, 264 density operator, 169–172, 175, 178, 309, 313–315

coherent-state representation, 175, 176, 179 P representation, 176, 178–180 reduced, 311 difusion, 67, 156, 253, 271, 327–329, 331, 386 equation, 386 phase, 386 dipole moment, permanent, 89, 91, 410, 411 dipole–dipole resonance interaction, 482–497 discrete-exponential distribution, 121 dispersion interaction, 409, 411, 417, 419, 420 bubbles, 424 in dielectric media, 423, 424 London, 411, 419 miscibility, 424 non-additivity, 420, 421 radiation reaction, 420 repulsive, 424 van der Waals, 416, 419, 420 dispersion-free ensemble, 315, 316 displacement current, 2 Doppler shift, 40, 43, 44, 116, 193 momentum exchange, 40 dressed states, 263, 269, 285, 286, 288, 289, 437

Earnshaw’s theorem, 4–6 efective noise intensity, 400 Einstein A coeficient, 111, 113, 114, 226, 228, 235, 250, 264, 280, 483 in a dielectric medium, 509, 510 Einstein B coeficient, 111, 113, 114 Einstein fluctuation formula, 69, 118, 120, 124 Einstein–Podolsky–Rosen paradox, 300, 307, 308, 312, 317 Einstein–Rupp experiment, 193 electric dipole approximation, 78, 84, 209–211, 255, 263 electric dipole interaction, 73–75, 213, 436 electromagnetic field uncertainty relations, 185, 188–190 electromagnetic mass, 221 electromagnetic momentum, 39–48 Eliezer-Landau–Lifshitz equation, radiation reaction, 375 energy–time uncertainty relation, 195, 201–203 Mandelstam–Tamm relation, 203 spectral widths, 201, 202 virtual processes, 201, 203 entanglement, 307–309, 311, 312, 317, 318, 483 entropy, 311, 312 Ewald–Oseen extinction theorem, 29, 31, 67 excess spontaneous emission factor, 390 exponential decay, 226, 229, 230, 232, 238–240, 248, 267, 268 extinction theorem, 28, 29, 31, 32, 67 Fano diagonalization, 463, 467–469, 471

Fermi approximation, 494, 495 Fick’s law, 328 fine structure, 94 fission. 4 fluctuation–dissipation theorem, 251–253, 325, 327, 345, 351, 353, 354, 356, 358–360, 364, 366–368, 378, 408, 409, 482 for electric field, 364 nonlinear systems, 364 Fock states, 151, 152, 160, 166, 172, 175, 177, 178, 275, 277–279, 297, 396 Fokker–Planck equation, 328–331, 335–337, 386 relation to Langevin equation, 335 F¨orster resonance energy transfer, 497–502 forward scattering amplitude, 63, 64 free energy, 366, 371, 376, 377, 420, 423, 475 gain coeficient, 105, 109, 380, 381, 384, 386, 387, 400 gauge invariance, 213, 216 gauge transformations, 6, 13, 139, 207, 233 restricted, 7 gauges, 6–15 Gaussian random process, 336, 342, 385 Gaussian statistics, 164, 177, 336, 338 generalized susceptibility, 358, 360 generating function, 173, 174, 396 Bose–Einstein distribution, 174, 396 Poisson distribution, 174, 396, 403 golden rule, 81, 107, 111, 354, 500, 501, 518519 Green function, 7, 31, 365, 472–475, 477–480, 482 advanced, 9 dyadic, 365, 472–474, 477 generalized susceptibility, 360 retarded, 8, 14, 20 tensor, 365 group index, 37, 39, 44, 46, 60, 142, 509 group velocity, 37, 42, 47, 142, 379–381 hairy ball theorem, 118 half-wave antenna, 17–19, 22 Hamilton’s principle, 74 Hamiltonian, electric dipole, 69, 70, 74–77, 84, 127, 211–216, 219, 223, 232, 233, 255, 257, 347, 486 Hamiltonian, minimal coupling, 73, 76–79, 89, 90, 127, 205–208, 210, 211, 213–216, 219, 221, 223, 232, 233, 262, 267, 268, 347, 420, 497 Hanbury Brown–Twiss efect, 69, 123, 124 classical explanation, 124, 125 Einstein fluctuation formula, 124 intensity interferometry, 125, 127 probability amplitudes, 127 Hannay’s theorem, 22, 67 heat bath, 359, 370, 371, 376, 420, 475

Index#

Heisenberg equation of motion, 72 Heisenberg picture, 72, 73, 83, 212, 223, 235, 238, 285, 307, 440, 441, 467, 488, 493, 506 helicity, 140 Hellmann–Feynman theorem, 421, 422, 476 Helmholtz equation, 133 Helmholtz free energy, 371 Helmholtz theorem, 13, 515 Henry parameter, 384 Hermitian operators, 199, 200, 208, 313, 315 completeness of eigenvectors, 70, 132 Hertz vector, 20, 32, 34 Hertzian dipole, 20 heterodyne detection, 406 hidden variables, 312, 317–321 locality, 318 von Neumann’s proof, 312, 313, 315, 316 homodyne detection, 406, 407 balanced, 407 homogeneous broadening, 107, 109 Hong–Ou–Mandel interferometer, 405 hyperfine structure, 94, 95 sodium D line, 95 ideal broadband detector, 518, 519 induction interaction, 410, 411 inhomogeneous broadening, 107 intensity correlations, 123 interaction picture, 71, 72, 153, 154, 307 Jaynes–Cummings model, 269, 274, 276, 277, 280–285 Jefimenko equations, 15 Johnson noise, 351–353, 356, 402 Nyquist formula, 351–353 Keesom dipole orientation interaction, 410 Klein–Nishina formula, 66 Kramers–Heisenberg dispersion formula, 87, 89, 103, 141, 412, 433, 438, 446 Kramers–Kronig relation, 39, 65, 362 Lagrangian, 73, 74, 205, 213 Lamb shift, 91, 223, 232, 233, 244, 262, 263, 274, 358, 373, 401, 412, 438–441 Welton’s model, 439 Landau terms, 264 Landau–Lifshitz equation, radiation reaction, 243, 372, 375 Langevin equation, 333–336, 341, 379 quantum, 341–346, 359, 371, 373, 375, 378, 379 relation to Fokker–Planck equation, 336 Langevin noise, 382, 383, 391, 392, 394, 460, 462, 467, 471 Larmor formula, 12, 21, 112 laser linewidth, 378–381, 384, 386–388, 390, 401 K factor, 390

amplitude-stabilized, 384–386 excess spontaneous emission factor, 390 gas lasers, 388 Henry parameter, 384 linewidth enhancement parameter, 384 Petermann factor, 390 phase-amplitude coupling, 387, 388 semiconductor lasers, 388 laser threshold, 159 laser, photon statistics, 156–159 Lebedev experiment, 44 Li´enard–Wiechert potentials, 10–12 Lifshitz theory of molecular forces between dielectrics, 409, 447, 449, 452, 454, 456, 458, 459, 472 stochastic electrodynamics, 471, 472 linewidth enhancement parameter, 388 local oscillator, 406, 407 longitudinal delta function, 184, 515, 516 Lorentz force, 42, 48, 49, 51, 53, 205 Lorentz gauge, 7, 13, 14, 20, 513, 514 Lorentz model, 27, 35 Lorentz transformation, 6, 7, 10, 11, 117 Lorentz–Lorenz formula, 29 Lorentz–Lorenz local field, 54 Lorentzian distribution, 173, 229 Lorentzian lineshape, 105, 109, 110, 229, 232, 235, 288, 380

Mandel Q parameter, 166, 178, 283, 297, 299, 300 Mandelstam–Tamm energy–time relation, 203 Markovian approximation, 226, 227, 234, 239, 247, 253, 258, 265, 270, 291, 329, 332, 371, 378, 489 mass renormalization, 65, 261, 262, 440 master equation, 328, 329, 331 Matsubara frequencies, 458 Maxwell stress tensor, 48, 448 Maxwell’s equations, 1, 2, 4, 6, 9, 11, 24, 30, 31, 49, 50, 69, 73, 80, 107, 133, 135, 138, 141, 214, 437, 441, 444, 446, 473 for field operators, 138, 209, 210, 236 Maxwell–Bartoli theory, 44 Maxwell–Bloch equations, 107 memory function, 349, 360, 371, 373 Mie scattering, 61 minimal coupling, 73, 76, 79, 89, 205–208, 210, 211, 213 Minkowski energy-momentum tensor, 52 Minkowski force density, 52 Minkowski momentum density, 40, 46, 51 Minkowski photon momentum, 452 Minkowski stress tensor, 49 mixed state, 170 momentum electromagnetic, 39–48 photon, 40–46, 48

multiple scattering, 61 milk, 62

negative oscillators, 101

neoclassical theory, 254, 255, 267

Nichols–Hull experiment, 44

no-cloning theorem, 310

noise figure, 391, 393, 394, 398, 400

noise polarization, 462, 465

noise power, 392, 397, 401, 402 per mode, 401

non-exponential decay, 239, 240

normal order, 169, 174–176, 179–181, 236, 242, 247, 248, 250, 257, 265, 297, 385, 388, 395, 396, 420, 440, 481, 489, 492, 516, 518, 519

Nyquist formula, 351–353, 402

observed mass, 221, 261, 374, 377 optical binding, 423 optical theorem, 62–65, 232, 376 orientation interaction, 410, 411 oscillator model of an atom, 99–101 oscillator strength, 27, 100, 101, 111, 112, 378, 415

P distribution, 177, 178, 180 P representation, 176, 178–180 Paley–Wiener theorem, 230 parametric down-conversion, 161 passive medium, 144 Pauli–Jordan commutation relations, 184 permanent dipole moment, 89, 91, 410, 411 phase velocity, 26, 28, 30–33, 41–43, 287, 380 phase-sensitive detection, 406 photodetection theory, 516–519 photoelectric efect, 69, 80–82, 120, 122 photon anti-bunching, 124, 269, 297–300 resonance fluorescence, 269, 297–299 photon bunching, 113, 122, 123, 166, 180, 181, 297, 299 photon counting, 145, 147, 156, 167, 168 photon momentum, 40–46, 48 Doppler shift, 40 photon polarization correlations, 301–305 photon spin, 139, 140 experimental proof, 140, 141 photon statistics, 174, 204, 392, 395 amplifier, 396, 397 attenuator, 395, 396 laser, 156–159 sub-Poissonian, 166, 283, 284 photons and interference, 144–146 experiment of G. I. Taylor, 146, 147 Planck spectrum, 112–117, 119–121, 138, 357, 366, 443 cosmic background radiation, 114 plasma frequency, 36 Poincar´e recurrence theorem, 282

Poisson distribution, 57, 119, 153, 156, 159, 165, 168, 279, 393, 395–397 generating function, 174

Poisson equation, 13, 208

Poisson statistics, 57, 392 amplifier, 394 attenuator, 394

Poisson summation formula, 348

polaritons, 143, 463, 471

polarizability, 26, 28, 34, 44, 46, 47, 53, 55, 58, 59, 62–65, 87–90, 103, 104, 141, 232, 288, 361, 375, 376, 410–412, 415, 420, 422, 423, 433–436, 438, 446, 475, 496

dielectric sphere, 34

ponderomotive potential, 88, 89, 128

power spectrum, 147, 291, 339–34

Poynting vector, 12, 16, 19, 20, 23, 37, 39, 50, 143

Poynting vector operator, 465

Poynting’s theorem, 36, 50, 143, 465 principle of least action, 73 probability amplitude, 124, 127, 192, 224, 233, 234, 236, 239, 303–305, 307, 405, 483, 484

projection operator, 170, 314

pulse area, 106

Purcell efect, 509

pure state, 170, 171, 199, 311, 312

purity, 171

Q factor, 509

Q parameter, 166, 178, 283, 297, 299, 300

quantum recurrence theorem, 281

quarter-wave antenna, 17

quiver energy, 89

Rabi frequency, 98, 102, 103, 271, 276, 277, 289, 290, 292, 296

generalized, 105

vacuum, 277, 282, 288

Rabi oscillations, 106, 111

radiation pressure, 44

radiation reaction, 65, 155, 188, 219–223, 239–244, 246, 249, 250, 254, 255, 265, 267, 357, 358, 371–373, 375, 376, 378, 388, 420, 424, 438, 489

Abraham–Lorentz equation, 371, 375

Eliezer equation, 373, 375

Ford–O’Connell theory, 325, 373–375

Lamb shift, 358, 373

Landau–Lifshitz equation, 243, 372, 373, 375

neoclassical theory, 254, 270

normal ordering, 242, 248, 250 radiative frequency shifts, 240, 241, 244, 247, 250

relation to vacuum field, 251, 252, 325

Index#

symmetric ordering, 246, 250 Raman–Bhagavantam experiment, 140 Rayleigh scattering, 21, 47, 54–56, 58, 59, 61, 63–65, 68 polarization by, 58, 59 Rayleigh–Jeans spectrum, 112, 113, 119 reactive fields, 19, 22 recoil, 42, 43, 46 in absorption and emission, 115 in spontaneous emission, 117 Planck spectrum, 113, 115–117 semiclassical theory, 82, 117 reduced density matrix, 309, 312 reduced matrix element, 93 remarkable formula for energy of oscillator interacting with heat bath, 370, 371, 376, 420, 475 renormalization, 65, 223, 261, 262, 440 resonance fluorescence, 269, 289, 291, 294–297, 339 revivals, 282, 283 rotating-wave approximation, 102, 237, 253, 264, 269, 271, 274, 275, 290, 291, 296, 298, 300, 302, 467, 490, 491, 496

saturation intensity, 110 scalar wave equation, 7 scattering force, 47, 63 Schawlow–Townes linewidth, 381, 388 Schmidt coeficients, 311, 312 Schmidt decomposition, 311, 312 Schr¨odinger picture, 71, 72, 81, 212, 223, 234, 238, 276, 307 selection rules, electric dipole transitions, 93, 96, 97 semiclassical radiation theory, 69, 76, 80, 82, 83, 107, 112, 117, 128, 185, 211, 253, 254, 257, 269, 271, 276, 279, 280, 286, 294, 299, 446 shot noise, 165 signal-to-noise ratio, 127, 391, 393, 398 simultaneous measurement of non-commuting observables, 200, 201 skylight polarization, 58 spectral density, 340 spontaneous absorption preclusion of, 250 spontaneous emission, 222, 379, 388, 390, 509, 510 amplified, 388, 390, 397–401 angular distribution, 118 factor, 379, 394, 398 in a dielectric medium, 509, 510 laser amplitude fluctuations, 384 local field correction, 509, 510 noise, 379, 382, 398 amplification, 390 amplified, 390, 398

noise operator, 379, 382, 383 phase fluctuations, 386 zero-point field, 244 spooky actions at a distance, 308 squeezed states, 159, 197 amplitude squeezing, 160 homodyne detection, 407 parametric down-conversion, 161 phase squeezing, 160 squeezed vacuum state, 160, 162 uncertainty relation, 160 Stark shift, 88–92, 104, 286, 287, 377, 420, 431, 434–436, 438, 496, 497 linear, 91 stationarity, 122, 178, 337–340 stimulated emission, 99, 109, 110, 113, 116, 117, 119, 156, 157, 159, 162, 244, 269, 271, 273, 274, 276, 290, 379, 380, 391, 395, 399, 519 as constructive interference efect, 271–273 classical, 273 cross section, 109 stochastic electrodynamics, 9, 268, 445, 446, 472 Stokes relations, 402 storage fields, 19, 21–23, 67, 502 stress tensor, 48–50, 52, 53 Minkowski, 49 structure factor, 56 sub-Poissonian photon statistics, 166, 283, 284 subradiance, 484, 487, 488 superradiance, 484, 487, 488 symmetric order, 179, 181, 242, 245–248, 250, 268, 412 thermal radiation, 123, 164, 166, 173, 177, 178, 244, 297, 402 Thomas–Reiche–Kuhn sum rule, 88, 89, 92, 101, 364 Thomson scattering, 65–67, 88 transverse delta function, 184, 216, 220, 515, 516 two-state atom, 97–109, 113, 223, 228, 234, 235, 243, 246–249, 253, 254, 274, 275, 277, 279, 282, 286, 291, 292, 297 experimental realization, 99 in derivation of Planck spectrum, 113 uncertainty relation, 132, 197 coherent states, 147 commutators, 182, 186 electromagnetic field, 185, 188–190 energy–time, 195 generalized, 198 harmonic oscillator, 132 interpretation, 199 molecular rotations, 133 not referring to the past, 203

Index

operational interpretation, 199 zero-point energy, 132

vacuum field, 246, 247 in photodetection theory, 520 radiative frequency shifts, 247, 250 spontaneous emission, 246 vacuum field fluctuations, 240, 244, 252, 255, 263, 265, 358, 389, 390, 419, 431, 435, 438–440, 442 amplification, 389, 390 Lamb shift, 439 vacuum Rabi frequency, 277, 282, 288 vacuum Rabi oscillations, 508 vacuum Rabi splitting, 288 van der Waals interaction, 409–417 Casimir–Polder, 416, 417, 419 London, 415, 416 modification by external fields, 423 nonretarded, 415, 416 repulsive, 424 retarded, 416, 417 temperature dependence, 422, 423 zero-point energy, 417–419 virial theorem, 3 von Neumann entropy, 171, 311

wave–particle duality, 118–120, 136, 144, 146, 193

Weisskopf–Wigner approximation, 226, 267, 485 Wien spectrum, 119 Wiener–Khintchine theorem, 147, 339, 340, 359, 380 Wigner–Eckart theorem, 93

Zeeman shift, 233 zero-point energy, 145, 216, 244, 245, 252, 263, 344, 356, 366, 409, 436, 438, 440–442 Casimir force, 425, 428, 429, 435, 438, 480 dissipative media, 464, 465, 467 Lamb shift, 439, 441 latent heat, 443 Lifshitz theory, 453, 454, 458, 480 liquid helium, 442 molecular spectra, 444 Planck spectrum, 443 reality of, 480, 482 Schwinger’s source theory, 481 specific heats, 443 stochastic electrodynamics, 446 uncertainty relation, 132, 442 van der Waals interaction, 417–419 zero-point energy, 419 x-ray difraction, 443