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Barnett S.M., Radmore P.M. Ч Methods in Theoretical Quantum Optics
Barnett S.M., Radmore P.M. Ч Methods in Theoretical Quantum Optics



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Ќазвание: Methods in Theoretical Quantum Optics

јвторы: Barnett S.M., Radmore P.M.

јннотаци€:

This work presents the mathematical methods widely used by workers in the field of quantum optics. Based on teachings by the authors, most of the text has been proven in extensive work with students.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: reprinted edition

√од издани€: 1997

 оличество страниц: 284

ƒобавлена в каталог: 10.04.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
A-coefficient      134 169
Above-threshold ionization      143
Absorption      19 22 24 166 176 186
Ackerhalt      217
Alternating symbol      223
Amplitude equations      5 11 15Ч19 21 27 132
Analytic continuation      141 205 246
Analytic function      89
Angular momentum, coherent state      80Ч86
Angular momentum, eigenstate      80
Angular momentum, operator      35 36 45Ч46 80 82 84 237
Angular momentum, vector      83
Annihilation operator      11Ч13 24 36 84 129 145 220
Annihilation operator for a quasi-mode      214Ч216
Annihilation operator in the Heisenberg picture      30Ч32 146 251
Annihilation operator, action on a coherent state      58 60
Annihilation operator, action on a number state      36
Annihilation operator, dressed      214Ч216
Annihilation operator, expressed in terms of number and phase operators      100
Annihilation operator, expressed in terms of quadrature operators      64
Annihilation operator, unitary transformation of      18 75 77
Anticommutator      4 47 224
Antinormal ordering      41 42 44 48 50 55 57 106 117 237
Associated Laguerre polynomial      28 111 114 231 254
Atomic coherent state      80Ч86
Atomic level      27 34
Atomic operator      153Ч156 159 165 256 see
Autler Ч Townes spectrum      186 187 208 213
Bare state      182Ч188 190 195Ч196 198 200Ч201 203 207 209
Beam-splitter      77 80 84 86 94
Bernoulli sampling      94Ч95
Bessel function      120 231Ч232
beta function      82 228Ч229
Binomial distribution      81 168
Binomial expansion      27 69 90
Binomial factor      86 94
Bixon Ч Jortner quasi-continuum      27Ч29 196Ч199
Black-body radiation      53
Bloch equations      170
Boltzmann's constant      53
Bose Ч Einstein distribution      54 57 92 95 156
Boson operators      52 53 56 66 77
Bra      1
Broad-band field      150 152 157
Bromwich contour      250
c-number Langevin equation      see "Langevin equation"
Cauchy residue theorem      245 248 250
Cauchy Ч Schwarz inequality      7
Cavity      145 148 213 215 217
Cavity mode      31 145Ч146 150Ч152 154 163 165Ч167 175 213 216 217
Characteristic function      106Ч114 116 117 119 122Ч123 125Ч129 178Ч179
Characteristics, method of      178 258Ч261
Classical current      178
Coherent amplitude      73
coherent interaction      14Ч34 132 186
Coherent squeezed state      72Ч75
Coherent state      57Ч67 88Ч89 112 117 167Ч168 239 see
Coherent state, conditioned density matrix for      175Ч176
Coherent state, moment generating function for      92 178
Coherent state, phase properties of      103Ч105
Collapse      25Ч27 189 217
Commutation relation      30 35 38 46 48 51 145 146 153 see
Commutation relation for continuum operators      38
Commutation relation for differential operators      266
Commutator      3Ч4 42Ч43 45 46 236 238 see
Commutator of angular momentum operators      35 237
Commutator of creation and annihilation operators      11 100
Commutator of creation and annihilation operators with the number operator      12 36
Commutator of dressed operators      214
Commutator of Langevin operators      148
Commutator of number and phase operators      98
Commutator of Pauli operators      35 224
Commutator of quadrature operators      37 234
Commutator, equal time      30 32 146 147 149
Commutator, involving continuum operators      38 48 51Ч52
Compatible      4
Complementary      96 98
Complete, basis      8 62
Complete, set      3Ч6 8 12 37 39 40 50 62 87 88 96 199 203 205 215
Conditioned, density matrix      175Ч176
Conditioned, evolution      174Ч176
Conditioned, wavefunction      176
conjugate      37 95Ч96 99
Conjugate, eigenvalue equation      2
Continuum, flat      132 135 143 206Ч208
Continuum, operator      13 38 39 42 47 48 51 56 78 79 236 237
Continuum, operator commutation relation      38
Continuum, squeezed vacuum state      79
Continuum, state      51 52 200 203 205 209
Continuum, state, amplitude      140Ч143
Continuum-continuum interactions      143
Contour integration      147 207 245Ч249
Convolution      23 116 252
Correlation      8 23 76 78 125
Correlation, function      55Ч56 152 155Ч160 164Ч165 172Ч173 180 221 272 274 275
Counter-rotating terms      32 33
Coupling      14 22 27 130 133 134 136 146 153 169 209
Coupling, constant      138 143 212 215 240
Coupling, effective      194
Coupling, Lorentzian      206Ч208
Creation operator      11Ч13 18 24 30Ч32 36 41 59 100 145 215
Creation operator, continuum      38 51Ч52 66 145 162 214
Cross-product      223
Cubic equation      191Ч192 276
Damped cavity mode      145 163 165 175
Damped cavity mode, annihilation operator      154
Damped harmonic oscillator      145 152
Damping      145Ч161 165 167 208 see
Damping, rate      137
Decorrelation      22Ч23 155Ч156 159 163Ч164 169 255Ч257 270
Delta function      22 135 173 204 225Ч227
Delta function, commutator      38
Delta function, derivatives of      118 121 123 227
Delta function, moment      56
Delta function, orthogonality      37 88 200
Delta function, three-dimensional      38 226Ч227
Delta function, two-dimensional      109 118 121 124
Density matrix      6 8 10 53Ч55 76 87 97 108 110 112 117 162Ч169 174Ч176
Determinant      183 191 273
Detuning      15 19 21 30 131 144 150 190
Diagonalization      182 200 207 209
Dielectric medium      14 32
Differential operator      178 263Ч265 266
Diffusion      179Ч180 266Ч268 273 274
Dipole      53 153 156 157 171 see
Dipole, matrix element      190
Dipole, moment      9 156 171
Dipole, operator      11 38
Dirac      95 201
Dirac, delta function      see "Delta function"
Displacement operator      43Ч44 57 106 112 122 126 see
Displacement operator, continuum      47 65
Displacement operator, functions of      63
Displacement operator, number state matrix elements of      113Ч114
Displacement operator, product of two displacement operators      62 65 78 85
Displacement operator, unitary transformation induced by      60 116 122
Dissipation      130Ч181
Double pole      249
Dressed, operator      213Ч221
Dressed, state      182Ч221
Drift term      179 266
Eigenfrequency      169 183 189 191Ч198
Eigenfrequency, operator      217Ч221
Eigenoperator equation      213Ч215 218Ч219
Eigenstate      2Ч5 12 36 37 51 58 65 80 96 182 see
Eigenvalue      2 3 5
Eigenvalue, equation      2 12 37 39 97 183 189 197
Einstein, A-coefficient      134 169
Einstein, rate      10 166
Electric Dipole      11 35 53
Electric dipole, approximation      11 35
Electric dipole, Hamiltonian      13
Electric dipole, interaction      14 18 38
electric field      13 15
Electric field, operator      13 38 216
electromagnetic field      1 10 13 14 24 87
Energy level      34 187
Ensemble average      3 269 272
Entangled state      8 24 76 126 128
Environment      53 130 145 161Ч163 165 168Ч169 174 176
Environment, operators      145Ч151 163Ч165
Excitation number      217
Excited state      10 83 152 156 206
expectation value      3 5 6 8 15 16 34 36 50
Exponential decay      14 29 132 133 144 146 195 208
Fabry Ч Perot, cavity      215
Fabry Ч Perot, mode functions      217
Factorial moment      90 92Ч95 111 119 178
Fano theory      200Ч213
Fermi Golden Rule      130Ч133
Fermi Ч Dirac statistics      53
Field, mode      12 17 29Ч33 53 61 237 238
Field, statistics      176Ч181
Final value theorem      140Ч145 206 250Ч254
Final-state spectrum      132 133 140 143 206 208 212Ч213
Fluctuations      22 23 145 216
Fluorescence      171 173 187
Fokker Ч Planck equation      179 266Ч275
Fourier transform      26 114 116 122 128 129 135
Free Hamiltonian      11
Frequency shift      33 134 136 137 151 154 157 165 195 201 206
Function of an operator      5 39
Functional derivative      47Ч50
Gamma function      228Ч229
Gaussian      26 64 71 72 75 103 104 116 122 123 125 226
Generalized function      37 115 116 118 127 179 see
Generating function      93 110 229 230 231 see
Glauber displacement operator      see "Displacement operator"
Glauber Ч Sudarshan P-representation      see "P-representation"
Green function      180 267Ч268
Ground state      83 152 186 198
Hamiltonian      5 11Ч13 16 32 39 53 129 145 153 162 180
Hamiltonian for free field      38
Hamiltonian for Jaynes Ч Cummings model      24
Hamiltonian for two interacting modes      29
Hamiltonian in interaction picture      16Ч18 85 163 168 180 190 196 198Ч199 200 203Ч204 209 214 215 253
harmonic oscillator      11 36 37 88 128 145 152 162
Heaviside function      see "Unit step function"
Heisenberg, equation      6 13 30Ч32 146 153 255Ч257
Heisenberg, picture      6 14 30 35 145Ч161 164 180 213
Heisenberg, uncertainty principle      see "Uncertainty principle"
Hermite polynomial      37 229
Hermitian, conjugate      2 4 6 9 68 77
Hermitian, operator      2Ч6 9 11 39 59 see
Hilbert space      37 95Ч96 100 103 105
Husimi function      119 see
Identity matrix      9 169 222
Identity operator      4 7 91
Identity operator, resolution of      4 12 37 61 74 81 87
Incompatible observables      1 4
Infinite series, summation of      248
Inner product      1 2
Interaction picture      14Ч18
Inverse      5 220 226
Inversion of transform      23 28 250Ч254
Inversion, atomic      9 34 53 152 156 171Ч172 195
Ionization      14 130 136Ч137 143 186 195 207
Jacobian      74
Jaynes Ч Cummings model      13 23Ч27 188 213 217 219
Joint, distribution      119
Joint, measurements      119
Kernel      22 23 135 148 149 154
Ket      1 7
Kronecker delta      3 90 222Ч224
Ladder system      190
Laguerre polynomial      28 110 113 230 232Ч233
LAMBDA system      190 195
Langevin, equation      148 180 269 271
Langevin, operator      148Ч149 154Ч157 159 164 256Ч257
Langevin, term      154 180 269 270 272 274 275
Laplace transform      20 23 27 120 133 138 144 146 250Ч254 see
Laser      57 136 137 144 169 186
Legendre polynomial      93Ч94 230
Liouville equation      163 169
Long-time limit      141 151 171
Lorentzian, continuum      206Ч209
Lorentzian, spectrum      23 142 145 160 161 209
Maclaurin expansion      39 267
Magnetic field      11 36 38
Markov approximation      135Ч136 147Ч149 151Ч152 154 156Ч157 159 165 256
Master equation      10 161Ч179 262Ч265
Matrix element      6 8 47 105 114 117 118 131 189 234 238 see "Number
Mean      3 6 36 54 102 149 221
Minimum uncertainty state      4 60 105
Mixed state      53 87 89 168 174
MODE      11Ч13 24 29Ч33 36 38 50 61 65 75Ч77 84Ч87 177 216Ч217 see "Field "Multimode" "Quasimode" "Single
Mollow spectrum      173Ч174 186Ч188
moment      42 50 54Ч56 79 89 96 100 110 115 121 149Ч150 see "p-ordered
Moment, generating function      89Ч95 108Ч109 119Ч120 122 125 177Ч178
Monochromatic field      11 14 15 18 130 190
Multimode states      125Ч129
Noisy fields      21Ч22
Non-classical, effect      161
Non-classical, state      29
Non-linear optics      14 29 30 67 76 179
Norm      51Ч53
Normal coordinates      273Ч274
Normal mode      32Ч33 274
Normal ordering      43Ч44 47Ч48 58 63 66 91 111 236Ч239
Normalization      7 51 87 203 210Ч111 225
Number operator      12 36 41Ч42 50Ч51 95Ч96 217 219 236
Number operator, continuum generalization of      39 51 53 56 66
Number operator, expectation value of      58 69 74
Number operator, moments of      54Ч55 59 76 89 98 100
Number operator, powers of      42 44
Number state      12 24 36 45 50Ч53 87 96 99 101 175
Number state, characteristic function of      109
Number state, displaced      62 88 117
Number state, matrix elements      97 113Ч114 239
Number state, P-representation of      118
Number state, Q-function for      121
Number state, quasi-probability distribution for      120
Observable      1 2 4Ч6 8 9 11 34 36 38 148 149 166 172 205 213
Off-diagonal damping      138Ч140 142 211
Optical resonance      213 217
Ordering      39Ч50 153 180 218 see "Normal "p-ordering" "Symmetric
Ordering in the Heisenberg equations      155 255Ч257
Ordering of differential operators      264
Ordering, theorems      39Ч50 236Ч239
Orthogonal      1Ч3 6 37 71 197 222
Orthogonality of functions      216 229 230
Orthonormal states      2Ч4 6 8 9 12 62 96 199
Orthonormality condition      201 214
Outer product      4
Overcomplete      51 61 74 81 88 96
Overlap      1Ч3 52 197 198
Overlap between a quadrature state and a coherent state      64 235
Overlap between a quadrature state and a number state      37
Overlap between a quadrature state and a squeezed state      72
Overlap between a squeezed state and a coherent state      71
Overlap between two angular momentum coherent states      81
Overlap between two coherent states      61
Overlap between two continuum coherent states      66
Overlap between two phase states      96
Overlap between two quadrature states      37
Overlap between two squeezed states      71
Overlap, integral      53
p-ordered moment      107Ч108 112 126 129
p-ordering      106Ч107
P-representation      117Ч118 120 121 127
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