Bibliography. Useful texbooks on theory, experiments, generation and applications of quantum squeezing.

Transcription

1 Bibliography Useful texbooks on theory, experiments, generation and applications of quantum squeezing. H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley, New York 1998) C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin Heidelberg New York 1990) C.W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin Heidelberg New York 2000) L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press Cambridge 1995) W. Schleich, Quantum Optics in Phase Space (Wiley, New York 2000) M.O. Scully and M.S. Zubairy, Quantum Optics (Cambridge University Press Cambridge 1997) W.Vogel, D.-G. Welsch and S. Wallentowitz, Quantum Optics: An Introduction (Wiley, New York 2001) D.F. Walls and G.,}. Milburn, Quantum Optics (Springer, Berlin Heidelberg New York 1994)

2 Index absorption spectrum, 264, 282 Airy function, 316 amplification without population inversion, 282 amplitude noise spectrum, 151, 165, 168 anomalous resonance fluorescence, 270, 273 antisymmetric state, attenuators, 94 beam splitter, 20, 75, 95, , 183, 184, 187, 188, 194, 195, 201, 212, 220,221 beam splitter transformation, 84 beam splitter transmittance, 178, 192 beam splitters, 83 Bell inequality, 349, 354, 356, 358, 359 bichromatic excitation, 295 Bloch-Siegert shift, 290 Bogoliubov transformation, 17 Born approximation, 315 boson vacuum state, 47 boundary terms, 113 Brillouin scattering, 127 broadband squeezed vacuum, 99, 266, 268,319 canonical commutation relations, 33, 53, 56, 62, 80, 82, 92, 173, 184 canonical momentum, 35, 41, 42, 80 canonical quantization, 33, 54, 55, 61, 173 canonical transformation, 11 causality, 57, 63, 71, 74, 82 causality condition, 61, causality conditions, 54, 73, 74 characteristic function, 9, 10 classical communication, 229, 230, 237, 246 classical dispersion theory, 41 classical feedback, 208 classical squeezing, 324, 331 classically squeezed field, 274 coherent states, 3, 13, 14, 17, 24, 26, 27, 29, 30, 228, 238, 240, 242, 247, 250,311 Coulomb gauge, 3, 4, 35-37, 173 coupling efficiency, 312, 313, 316, 319 critical fluctuations, 122 critical point, 109 density matrix, 104 density operator, 8, 9, 16, 20-22, 27, 208, 301, 315, 316 Dicke model, dielectric, 33, 34 Dimensionality Theorem, 234 Dirac delta function, 61 dispersion, 34, 39, 41, 46, 49, 284 dispersion relations, 45 displaced squeezed vacuum, 19 displaced squeezed vacuum state, 19 displacement operator, 9, 10, 14, 17 dressed states, 272, 273, Einstein's causality, 340 entanglement, 199, , 341, 343, 346, , , 359 entropy, 238, 239, 242 entropy bound, 242, 243 EPR paradox, 338, 339, 341, 342, 345, 348, 349, 355, 356 Euclidean distance, 234 Euclidean space, 234 Euclidean structure, 234

3 368 Index Euler-Lagrange equation, 55, 61, 174 Fabry-Perot cavity, 264, 282 Fabry-Perot microcavity, 293 feedback, , 175, 177, , , 199, , 215, 217, , 223, 243, 361 feedback master equation, 173, 211 feedback operator, 205 feedforward, 196, 220 Feynman diagram, 136 finite bandwidth, 266, 268, 282, 297. finite bandwidth squeezed light, 282 Fock states, 12, 13, 16, 19-22, 24, 25 Gaussian fluctuations, 185 Gaussian function, 29 Gaussian probability distribution, 59 Gaussian squeezed displaced states, 18 Glauber-Sudarshan P function, 113, 172 Glauber-Sudarshan P representation, 112 Gordon-Haus effect, 135 Hamiltonian density, 56 harmonic oscillators, 3 hidden variable theory, 356 hidden variables, 337, 339, , 354, 356, 357 hole-burning, 264, 293, 296 Holstein - Primakoff representation, 47 homo dyne detection, 19, 54, 74, 177, 184, 192, 193, 201, 206, 208, 212, 219, 240 homo dyne mediated feedback, 209 homodyne tomography, 11, 12 homodyne-mediated feedback, 202, 205, 207 Hopfield's theory, 45, 46 ideal squeezed vacuum, 267, , 284, , 292, 296, 301, 303 in-loop squeezing, 173, 188, 212, 213, 216, 218, 219 incoherent resonance fluorescence, 278 input-output, 107 intelligent states, 7 Jaynes-Cummings Hamiltonian, 144, 211 Jaynes-Cummings model, 23 Lagrangian density, 41, 42, 45, 55, 61, 173 Laguerre polynomial, 12, 22 laser phase diffusion, 152 Laser rate equations, 147, 148 Lie algebra, 7 linear dispersion, 39 linear feedback, 191 linear susceptibility, 38 Liouville equation, 205, 315 local hidden variables, 356 local realism, , 346, 348, 349, , 361 Mach-Zehnder interferometer, 213 macroscopic entanglement, 357 macroscopic local realism, 357, 358 Mandel Q-parameter, 21, 28, 29 Markov approximation, 54, 63, 64, 68, 70, 72, 74, 144, 318 Markovian feedback, 172 master equation, 104, 142, 172, 191, , 204, , 216, 218, , 302, 303, 312, 313, , 323 Maxwell's equations, 33, 34, 40, 50 minimum uncertainty state, 7 minimum uncertainty states, 8, 14 mode function, 316 mode functions, 38, 39, 87 multi-mode operator, 21 narrowband squeezed vacuum, 99, 266 noise spectra, 151 nonclassical field, 267 noncommuting observables, 6 nonlinear optics, 99 nonlinear Schrodinger equation, 125 number state, 12, 24, 30, 239, 240, 242, 244, 245, 250, 253, 254, 339 number states, 23, 227, 228, 242, 243, 250 optical Bloch equations, 268, 296 optical fibers, 123, 132 optimum squeezing, 121, 280

4 Index 369 Ornstein - Uhlenbeck equation, 204, 205 pairwise atomic state, 301, 304, 305 pairwise atomic states, 301 parametric amplification, 100 parametric amplifier, 73, 207, 327 parametric amplifiers, 53 parametric down conversion, 195, 196 parametric waveguide, 127 Pauli matrices, 266, 269, 278 phase noise spectrum, 154 phase shifters, 54, 82, 83 phase-space, 3, 8, 16 photodetection, 176, 191, 219, 220 photodetection operators, 201 photon current, 74, 77 photon current operator, 74, 76 photon flux, 76, 149, 176, 201, 217 photon number distribution, 16, 19, 27, 28 photon number operator, 5, 12, 13 photon-anti bunching, 99 Poisson ian distribution, 14 population trapping, , 301 positive P-representation, 112 pulsed lasers, 131 Pure atomic states, 277 pure state, 9, , 288, 300, 301 pure states, 8 purity, 278, quadrature, 105 quadrature probability distributions, 10 quadrature squeezing, 3, 7, 19, 23, 28, 30, 218, 246 quantized electromagnetic field, 6 quantum amplifier, 248 quantum amplifiers, , 248 quantum beats, 312, 324, 327, 328, 333 quantum causality, 71 quantum communication, 229, 237, 238, 249 quantum communications, 237, 244 quantum cryptography, 239, 337, 339, 342, 358, 359 quantum feedback, 172 quantum fluctuations, 3, 6, 7, 30, 77, 112, 187, 188 quantum interference, 21, 22, 24, 26, 30, 312, quantum interferences, 24, 333 quantum Langevin equations, 104 quantum noise, 153 quantum noise level, 152 quantum noise limit, 141 quantum non demolition experiment, 338 quantum nondemolition measurement, 33, 245, 247, 265, 338 quantum nonlinear Schrodinger equation, 125, 126 quantum optical feedback, 178 quantum teleportation, 339, 349, 359 quantum trajectories, 197 Raman lasers, 163 Raman scattering, 127 rate matching, 154, 155 rate-distortion function, 251 reservoir, 21, 143, 144, 157, 265, 311, 315, 316 resonance fluorescence, 263, 270, 272, 280, 282, 283, 293, 295, 297, 329 resonance fluorescence spectra, 271, 273, , 297 resonance fluorescence spectrum, 270, 271, 274, 276, , 295 resonators, 85 scattering matrices, 72 Schrodinger cat, 357, 358 secular approximation, 272, , 297 Shannon entropy, 230, 232 signal-to-noise ratio, 264 single-mode interferometer, 100 solitons, 132 spin operators, 47 spontaneous emission, 145, 155, 161, 165, 264, 281, 292, 293, 297, 322 spontaneous emission noise, 153, 161, 281 spontaneous emission rate, 319 squashed light, 185, , 325 squeezed light, 30, 191, 194, 207, 213, 217, 219, 221, , 268, 272, 291,

5 370 Index , 297, 299, 300, , 326, 330, 333, 344, 345 squeezed reservoir, 312 squeezed states, 3, 15, 17, 18, 171, 207, 227, 229, , 235, 237, 239, , 245, 247, 249, 251, 253, 255, 257, 259, 261 squeezed vacuum, 17, 19, 21, 210, , 277, 278, 281, 282, , , , 301, 302, 312, 313, 316, 317, , 327, 329, 330, 332 squeezed vacuum state, 15-18, 29 squeezing, 99 squeezing experiments, 122 squeezing spectrum, 106, 117, 281 standard quantum limit, 23, 177, 214, 219, 229, 245 stationary lineshape, 329, 330 stochastic differential equations, 113 stochastic increment, 202 stochastic master equation, 201, 202, 211, 215 SU(l,l) Lie algebra, 16, 19, 20 sub-poissonian photon number distribution, 19 sub-poissonian photon statistics, 21, 29, 30, 33, 99, 264 subnatural features, 271 subnatural linewidths, 269, 272, 275, 282, 296, 312 susceptibility tensors, 36 three-dimensional reservoir, 315 three-level system, 313, 328 transverse functions, 38 two-level atom, 266, , 278, 280, 290, 291, 293, 295, , 323, 324, 329 two-level atoms, 278, 290, 300, 301, 333 two-mode squeezed states, 358 two-mode squeezed vacuum, 19, 20, 297,304 two-mode squeezed vacuum state, 20 two-photon coherent state, 227 two-photon coherent states, 17 two-photon correlations, 265, 267, 292, 299, 323, 324, 330, 331, 333 two-photon population inversions, 300 uncertainty principle, 7, 154, 187, 193, 210, 255, 256, 337 uncertainty principles, 253 unconditioned master equation, 201 unitary operator, 11, 19 vacuum state, 3, 12, 13, 17, 23, 24, 43, 56, 7~ 79, 190, 194, 198, 311, 317 vector potential, 3-5, 33, 35, 37, 45, 173,175 Von Neumann entropy, 243 waveguides, 123 Weyl-Heisenberg algebra, 3, 7, 8 white noise process, 214 Wiener increment, 190, 202 Wigner function, 3, 8-15, 17-19, 22, 24-28, 204, 205, 354, 356, 357 Wigner representation, 132

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