| Foreword |
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xi | |
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| Preface |
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xiii | |
| Acknowledgments |
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xv | |
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1 Models of Two-Quantum Interaction of Non-Equilibrium System with Bath |
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1 | (30) |
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1 | (1) |
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1.1 Two Photon Cooperative Emission |
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2 | (7) |
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1.2 Two-Quantum Interaction of the System with Coherent and Squeezed Fields |
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9 | (5) |
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1.3 Two Quantum Generation in Micro-Cavities |
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14 | (5) |
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1.3.1 Two-Photon Emission from Excited Ridberg Atoms in Micro-Cavity |
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14 | (2) |
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1.3.2 Non-Linear Optical Parametric Down Conversion in Micro-Cavities |
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16 | (3) |
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1.4 Effective Hamiltonian of Two-Phonon Interaction of Electrons with Lattice Vibration |
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19 | (12) |
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25 | (6) |
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2 Methods of Elimination of Boson Field Operators in Two-Quantum Interaction with Vacuum and Squeezed Bath |
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31 | (58) |
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31 | (1) |
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2.1 Master Equation for Two-Photon Cooperative Decay in Interaction with Vacuum of EMF |
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32 | (10) |
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2.2 Hamiltonian and Master Equation in Cooperative Resonance |
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42 | (25) |
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2.2.1 Appendix 1: Elimination of Bi-Boson EMF Operators |
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52 | (8) |
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2.2.2 Appendix 2: Exchange Integrals |
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60 | (7) |
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2.3 Two-Photon Cooperative Interaction of Atomic Subsystem with Broadband Squeezed EMF |
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67 | (11) |
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2.4 Master Equation for Dipole Forbidden System Interacting with Coherent Displacement Squeezed Field |
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78 | (11) |
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86 | (3) |
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3 Elimination of Boson Field Operators in Nonlinear Interaction of Small System with Thermal Bath |
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89 | (40) |
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89 | (1) |
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3.1 Two-Photon Cooperative Interaction with Thermal Bath |
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90 | (6) |
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3.2 Master Equation for Two-Photon Cooperative Emission in the Microcavities (Bad Cavity Limit) |
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96 | (8) |
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3.3 Master Equation for Two-Phonon Collective Effects between the Electrons |
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104 | (7) |
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3.4 Correlation between Single and Two-Quantum Exchange Integrals |
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111 | (18) |
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126 | (3) |
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4 Procedure of Elimination of Bi-Boson Atomic (or Field) Operators in the "Good" (or "Bad") Cavity Limit |
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129 | (32) |
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129 | (1) |
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4.1 Master Equation for Cavity Sub-Harmonic Field |
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130 | (4) |
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4.2 Master Equations of Small Subsystems in Two-Quantum Interaction |
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134 | (8) |
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4.3 Cooperative Quantum Theory of Two-Photon Generation with Losses in Photon Pairs |
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142 | (6) |
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4.4 Cooperative Theory in Raman Lasers |
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148 | (5) |
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4.5 Cooperative Lasing in the Hyper-Raman Process |
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153 | (8) |
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158 | (3) |
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5 Representation of Photon Correlation Functions through Atomic Correlations |
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161 | (32) |
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161 | (1) |
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5.1 The Photon Correlation Function in Two-Quantum Detection |
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162 | (3) |
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5.2 The Representation of Photon Correlation Functions through Sours Correlations |
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165 | (6) |
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5.3 The Representation of Photon Correlation Functions in Two-Photon Interaction of Laser Field with Radiators |
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171 | (6) |
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5.4 Amplitude-Squared Squeezing in Intense Two-Photon Resonance Field |
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177 | (4) |
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5.5 The Quantum Fluctuation in the External Thermal Field |
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181 | (3) |
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5.6 Lithographic Limit and Problems of Two-Photon Holograms in Quantum Optics |
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184 | (9) |
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189 | (4) |
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6 Fokker-Planck Equations and their Steady State Solutions. Induced Phase Transitions |
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193 | (36) |
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193 | (1) |
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6.1 The Fokker-Planck Equation for Two-Photon Super-Radiance in the Presence of Thermal Field |
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193 | (8) |
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6.2 su(2) Complex P Representation. Fokker-Planck Equations and Its Steady State Solutions |
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201 | (12) |
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6.3 Fokker-Planck Equation for su(1, 1) Algebra and Its Steady State Solution |
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213 | (4) |
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6.4 Q Representation for su(1, 1) and Fokker-Planck Equation |
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217 | (12) |
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225 | (4) |
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7 Two-Quantum Superradiance and Its Mutual Interaction with Single-Photon Superfluorescence |
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229 | (50) |
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229 | (1) |
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7.1 Two-Photon Super-Radiances of Inverted Atomic System |
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230 | (8) |
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7.2 Photon Correlations in Tow-Quantum Super-Radiance |
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238 | (3) |
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7.3 Mutual Influence of Single- and Two-Photon Cooperative Spontaneous Emission |
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241 | (11) |
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7.4 Two-Photon Cooperative Emission of Three Radiators |
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252 | (3) |
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7.5 Two-Photon Collective Resonance Fluorescence |
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255 | (12) |
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7.6 Two-Photon Supper-Radiance in the Interaction of Atomic Stream with Thermal Field |
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267 | (4) |
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7.7 Two-Photon Cooperative Emission in Microcavities |
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271 | (8) |
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276 | (3) |
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8 Cooperative Two-Quantum Lasing and Steady State Solution of Master Equations |
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279 | (28) |
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279 | (1) |
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8.1 Coherent Generation of Photon Pairs by Atomic Stream |
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280 | (5) |
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8.2 Quantum and Semi-Classical Approach for Two-Photon Generation with Pears Losses from Resonator |
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285 | (6) |
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8.3 Quantum Solution of Master Equation for Raman Lazing Process |
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291 | (7) |
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8.4 Cooperative Quantum Correlations Between Stokes and Anti-Stokes Modes in Four Wave Mixing |
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298 | (9) |
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8.4.1 Semi Classical Approach |
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298 | (3) |
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8.4.2 Quantum Description: The Quantum Solution of Master Equation |
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301 | (3) |
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304 | (3) |
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9 Nonlinear Effects in Cooperative Second Order Phase Transitions |
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307 | (18) |
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307 | (1) |
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9.1 Two-Quanta Super-Radiant Phase Transition |
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308 | (6) |
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9.2 Temperature Dependence of Order Parameter in Nonlinear Superconductivity |
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314 | (11) |
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321 | (4) |
| Index |
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325 | |
