R.R.Puri MATHEMATICAL METHODS OF QUANTUM OPTICS Berlin: Springer, 2001, pp.. XIII+285 This book provides an accessible introduction to the mathematical methods of quantum optics.. Star
Trang 1R.R.Puri
MATHEMATICAL METHODS OF QUANTUM OPTICS
Berlin: Springer, 2001, pp XIII+285
This book provides an accessible introduction to the mathematical methods of
quantum optics Starting from first principles, it reveals how a given system of atoms
and a field is mathematically modelled The method of eigenfunction expansion and the
Lie algebraic method for solving equations are outlined Analytically exactly solvable
classes of equations are identified The text also discusses consequences of Lie
algebraic properties of Hamiltonians, such as the classification of their states as
coherent, classical or non-classical based on the generalized uncertainty relation and the
concept of quasiprobability distributions A unified approach is developed for
determining the dynamics of two-level and a three- level atom in combinations of
quantized fields under certain conditions Simple methods for solving a variety of linear
and nonlinear dissipative master equations are given
Contents
2.3.2 The SU(2) Algebra 42
Trang 22.3.5 The SU(m, n) Algebra 45
2.4.2 The SU(2) Algebra 50
4.3 Quasiprobabilitiy Distributions for Eigenvalues of Spin Components 93
5.7.1 Univariate Linear Multiplicative Stochastic Differential Equations 113
5.7.2 Multivariate Linear Multiplicative Stochastic Differential Equations 114
5.9 Stochastic Differential Equation Driven by Random Telegraph Noise 116
www.pdfgrip.com
Trang 36.1 Free Classical Field 119
8.8 Master Equation for Field Interacting with a Reservoir of Atoms 174
9 Linear and Nonlinear Response of a System in an External Field 177
10 Solution of Linear Equations: Method of Eigenvector Expansion 185
www.pdfgrip.com
Trang 410.2 Generalized Eigenvalues and Eigenvectors 189
10.4 Exactly Solvable Two- and Three-Term Recursion Relations 19210.4.1 Two- Term Recursion Relations 192
11 Two-Level and Three-Level Hamiltonian Systems 199
12.1.1 Time-Dependent Evolution Operator Reducible to SU(2) 217
13.1.1 Averages and Variances of the Cavity Field Operators 240
Trang 5D Roots of a Polynomial 273References 277
Index absorption spectrum 182
density operator 21 Descarte's rule 277 detailed balance 106, 108, 160, 225 differentiation, parametric 8
- of exponential operator 37
- of operator product 8 disentangling an exponential 48
- harmonic oscillator algebra 49
- SU(1,1) algebra 51
- SU(2) algebra 50
down conversion 151,239 dressed states 204
- correlation functions, classical 123
- correlation functions, quantum 130
- quantization 121 effective two-level approximation 212 effective two-level atom 147
eigenvalue 7,186
- generalized 189 eigenvector 7,186
- generalized 189 entangled state 20, 25 EPR Paradox 32 equal variance minimum uncertainty state 13
Fokker-Planck equation 107
www.pdfgrip.com
Trang 6- for spins 91 parametric processes 150 phase
- dynamic 16
- geometric (see geometric phase) 16 photon 122
Poisson process 115 probability amplitude 11 probability density 11,99
- conditional 103
- joint 99 pure state 22 Q-function 87
- for spins 92 quantum eraser 29 quasiprobability distribution 83
- for spins 89 Rabi frequency 142, 221 random telegraph noise 116 regression theorem 105,163 representations
- by eigenvectors 55
- equivalent 56
- labeled by group parameters 56
- of harmonic oscillator algebra 60
- of SU(1,1) algebra 76
- of SU(2) algebra 68
resonance approximation 144 resonance fluorescence 171, 219
- collective 225 rotating wave approximation 143, 181 Rydberg atom 152
s-ordering 83 Schmidt decomposition 25 Schrödinger equation 13 Schwarz inequality 2
- generalized 3
www.pdfgrip.com
Trang 7145 time-ordered exponential integration
- harmonic oscillator algebra 52
- SU(1,1) algebra 53
- SU(2) algebra 53
trace 6 transition probability 103 two-channel Raman-coupled model
150, 207 two-level atom 144 two-photon process 146 two-photon reservoir
- in ladder configuration 245
- in Lambda configuration 248 uncertainty relation 12
uncorrelated equal variance minimum uncertainty state 13, 62
vacuum field Rabi oscillations 205 vacuum field Rabi splitting 257 vacuum fluctuations 122
wave mixing 149, 181 wave-particle duality 26 welcher weg 28
which path 28 Wiener process 110, 111 Wiener-Khintchine theorem 136 Wigner function 87
- for spins 92 Zeno effect 16
www.pdfgrip.com
Trang 8www.pdfgrip.com
Trang 9www.pdfgrip.com
Trang 10www.pdfgrip.com
Trang 11www.pdfgrip.com
Trang 12www.pdfgrip.com
Trang 13www.pdfgrip.com
Trang 14www.pdfgrip.com
Trang 15www.pdfgrip.com
Trang 16www.pdfgrip.com
Trang 17www.pdfgrip.com
Trang 18www.pdfgrip.com
Trang 19www.pdfgrip.com
Trang 20www.pdfgrip.com
Trang 21www.pdfgrip.com
Trang 22www.pdfgrip.com
Trang 23www.pdfgrip.com
Trang 24www.pdfgrip.com
Trang 25www.pdfgrip.com
Trang 26www.pdfgrip.com
Trang 27www.pdfgrip.com
Trang 28www.pdfgrip.com
Trang 29www.pdfgrip.com
Trang 30www.pdfgrip.com
Trang 31www.pdfgrip.com
Trang 32www.pdfgrip.com
Trang 33www.pdfgrip.com
Trang 34www.pdfgrip.com
Trang 35www.pdfgrip.com
Trang 36www.pdfgrip.com
Trang 37www.pdfgrip.com
Trang 38www.pdfgrip.com
Trang 39www.pdfgrip.com
Trang 40www.pdfgrip.com
Trang 41www.pdfgrip.com
Trang 42www.pdfgrip.com
Trang 43www.pdfgrip.com
Trang 44www.pdfgrip.com
Trang 45www.pdfgrip.com
Trang 46www.pdfgrip.com
Trang 47www.pdfgrip.com
Trang 48www.pdfgrip.com
Trang 49www.pdfgrip.com
Trang 50www.pdfgrip.com
Trang 51www.pdfgrip.com
Trang 52www.pdfgrip.com
Trang 53www.pdfgrip.com
Trang 54www.pdfgrip.com
Trang 55www.pdfgrip.com
Trang 56www.pdfgrip.com
Trang 57www.pdfgrip.com
Trang 58www.pdfgrip.com
Trang 59www.pdfgrip.com
Trang 60www.pdfgrip.com
Trang 61www.pdfgrip.com
Trang 62www.pdfgrip.com
Trang 63www.pdfgrip.com
Trang 64www.pdfgrip.com
Trang 65www.pdfgrip.com
Trang 66www.pdfgrip.com
Trang 67www.pdfgrip.com
Trang 68www.pdfgrip.com
Trang 69www.pdfgrip.com
Trang 70www.pdfgrip.com
Trang 71www.pdfgrip.com
Trang 72www.pdfgrip.com
Trang 73www.pdfgrip.com
Trang 74www.pdfgrip.com
Trang 75www.pdfgrip.com
Trang 76www.pdfgrip.com
Trang 77www.pdfgrip.com
Trang 78www.pdfgrip.com
Trang 79www.pdfgrip.com
Trang 80www.pdfgrip.com
Trang 81www.pdfgrip.com
Trang 82www.pdfgrip.com
Trang 83www.pdfgrip.com
Trang 84www.pdfgrip.com
Trang 85www.pdfgrip.com
Trang 86www.pdfgrip.com
Trang 87www.pdfgrip.com
Trang 88www.pdfgrip.com
Trang 89www.pdfgrip.com
Trang 90www.pdfgrip.com
Trang 91www.pdfgrip.com
Trang 92www.pdfgrip.com
Trang 93www.pdfgrip.com
Trang 94www.pdfgrip.com
Trang 95www.pdfgrip.com
Trang 96www.pdfgrip.com
Trang 97www.pdfgrip.com
Trang 98www.pdfgrip.com
Trang 99www.pdfgrip.com
Trang 100www.pdfgrip.com
Trang 101www.pdfgrip.com
Trang 102www.pdfgrip.com
Trang 103www.pdfgrip.com
Trang 104www.pdfgrip.com
Trang 105www.pdfgrip.com
Trang 106www.pdfgrip.com
Trang 107www.pdfgrip.com
Trang 108www.pdfgrip.com
Trang 109www.pdfgrip.com
Trang 110www.pdfgrip.com
Trang 111www.pdfgrip.com
Trang 112www.pdfgrip.com
Trang 113www.pdfgrip.com
Trang 114www.pdfgrip.com
Trang 115www.pdfgrip.com
Trang 116www.pdfgrip.com
Trang 117www.pdfgrip.com
Trang 118www.pdfgrip.com
Trang 119www.pdfgrip.com
Trang 120www.pdfgrip.com
Trang 121www.pdfgrip.com
Trang 122www.pdfgrip.com
Trang 123www.pdfgrip.com
Trang 124www.pdfgrip.com
Trang 125www.pdfgrip.com
Trang 126www.pdfgrip.com
Trang 127www.pdfgrip.com
Trang 128www.pdfgrip.com
Trang 129www.pdfgrip.com
Trang 130www.pdfgrip.com
Trang 131www.pdfgrip.com
Trang 132www.pdfgrip.com
Trang 133www.pdfgrip.com
Trang 134www.pdfgrip.com
Trang 135www.pdfgrip.com
Trang 136www.pdfgrip.com
Trang 137www.pdfgrip.com
Trang 138www.pdfgrip.com
Trang 139www.pdfgrip.com
Trang 140www.pdfgrip.com
Trang 141www.pdfgrip.com
Trang 142www.pdfgrip.com
Trang 143www.pdfgrip.com
Trang 144www.pdfgrip.com
Trang 145www.pdfgrip.com
Trang 146www.pdfgrip.com
Trang 147www.pdfgrip.com
Trang 148www.pdfgrip.com
Trang 149www.pdfgrip.com
Trang 150www.pdfgrip.com
Trang 151www.pdfgrip.com
Trang 152www.pdfgrip.com
Trang 153www.pdfgrip.com
Trang 154www.pdfgrip.com
Trang 155www.pdfgrip.com
Trang 156www.pdfgrip.com
Trang 157www.pdfgrip.com
Trang 158www.pdfgrip.com
Trang 159www.pdfgrip.com
Trang 160www.pdfgrip.com
Trang 161www.pdfgrip.com
Trang 162www.pdfgrip.com
Trang 163www.pdfgrip.com
Trang 164www.pdfgrip.com
Trang 165www.pdfgrip.com
Trang 166www.pdfgrip.com
Trang 167www.pdfgrip.com
Trang 168www.pdfgrip.com
Trang 169www.pdfgrip.com
Trang 170www.pdfgrip.com
Trang 171www.pdfgrip.com
Trang 172www.pdfgrip.com
Trang 173www.pdfgrip.com
Trang 174www.pdfgrip.com
Trang 175www.pdfgrip.com
Trang 176www.pdfgrip.com
Trang 177www.pdfgrip.com
Trang 178www.pdfgrip.com
Trang 179www.pdfgrip.com
Trang 180www.pdfgrip.com
Trang 181www.pdfgrip.com
Trang 182www.pdfgrip.com
Trang 183www.pdfgrip.com
Trang 184www.pdfgrip.com
Trang 185www.pdfgrip.com
Trang 186www.pdfgrip.com
Trang 187www.pdfgrip.com
Trang 188www.pdfgrip.com
Trang 189www.pdfgrip.com
Trang 190www.pdfgrip.com
Trang 191www.pdfgrip.com
Trang 192www.pdfgrip.com
Trang 193www.pdfgrip.com
Trang 194www.pdfgrip.com
Trang 195www.pdfgrip.com
Trang 196www.pdfgrip.com
Trang 197www.pdfgrip.com
Trang 198www.pdfgrip.com
Trang 199www.pdfgrip.com
Trang 200www.pdfgrip.com
Trang 201www.pdfgrip.com
Trang 202www.pdfgrip.com
Trang 203www.pdfgrip.com
Trang 204www.pdfgrip.com
Trang 205www.pdfgrip.com
Trang 206www.pdfgrip.com
Trang 207www.pdfgrip.com
Trang 208www.pdfgrip.com
Trang 209www.pdfgrip.com
Trang 210www.pdfgrip.com
Trang 211www.pdfgrip.com
Trang 212www.pdfgrip.com
Trang 213www.pdfgrip.com
Trang 214www.pdfgrip.com
Trang 215www.pdfgrip.com
Trang 216www.pdfgrip.com
Trang 217www.pdfgrip.com
Trang 218www.pdfgrip.com
Trang 219www.pdfgrip.com
Trang 220www.pdfgrip.com
Trang 221www.pdfgrip.com
Trang 222www.pdfgrip.com
Trang 223www.pdfgrip.com
Trang 224www.pdfgrip.com
Trang 225www.pdfgrip.com
Trang 226www.pdfgrip.com
Trang 227www.pdfgrip.com
Trang 228www.pdfgrip.com
Trang 229www.pdfgrip.com
Trang 230www.pdfgrip.com
Trang 231www.pdfgrip.com
Trang 232www.pdfgrip.com
Trang 233www.pdfgrip.com
Trang 234www.pdfgrip.com
Trang 235www.pdfgrip.com
Trang 236www.pdfgrip.com
Trang 237www.pdfgrip.com
Trang 238www.pdfgrip.com
Trang 239www.pdfgrip.com
Trang 240www.pdfgrip.com
Trang 241www.pdfgrip.com
Trang 242www.pdfgrip.com
Trang 243www.pdfgrip.com
Trang 244www.pdfgrip.com
Trang 245www.pdfgrip.com
Trang 246www.pdfgrip.com
Trang 247www.pdfgrip.com
Trang 248www.pdfgrip.com
Trang 249www.pdfgrip.com
Trang 250www.pdfgrip.com
Trang 251www.pdfgrip.com
Trang 252www.pdfgrip.com
Trang 253www.pdfgrip.com
Trang 254www.pdfgrip.com
Trang 255www.pdfgrip.com
Trang 256www.pdfgrip.com
Trang 257www.pdfgrip.com
Trang 258www.pdfgrip.com
Trang 259www.pdfgrip.com
Trang 260www.pdfgrip.com
Trang 261www.pdfgrip.com
Trang 262www.pdfgrip.com
Trang 263www.pdfgrip.com
Trang 264www.pdfgrip.com
Trang 265www.pdfgrip.com
Trang 266www.pdfgrip.com
Trang 267www.pdfgrip.com
Trang 268www.pdfgrip.com
Trang 269www.pdfgrip.com
Trang 270www.pdfgrip.com
Trang 271www.pdfgrip.com
Trang 272www.pdfgrip.com
Trang 273www.pdfgrip.com
Trang 274www.pdfgrip.com
Trang 275www.pdfgrip.com
Trang 276www.pdfgrip.com
Trang 277www.pdfgrip.com
Trang 278www.pdfgrip.com
Trang 279www.pdfgrip.com
Trang 280www.pdfgrip.com
Trang 281www.pdfgrip.com
Trang 282www.pdfgrip.com
Trang 283www.pdfgrip.com
Trang 284www.pdfgrip.com
Trang 285www.pdfgrip.com
Trang 286www.pdfgrip.com
Trang 287www.pdfgrip.com
Trang 289www.pdfgrip.com
Trang 290www.pdfgrip.com
Trang 291www.pdfgrip.com
Trang 292www.pdfgrip.com
Trang 293www.pdfgrip.com
Trang 295www.pdfgrip.com
Trang 296www.pdfgrip.com
Trang 297www.pdfgrip.com
Trang 298www.pdfgrip.com
Trang 300www.pdfgrip.com
Trang 301www.pdfgrip.com
Trang 302www.pdfgrip.com
Trang 303www.pdfgrip.com