| Preface |
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v | |
| PART I. Theory of the interaction between atom and radiation field |
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3 | (132) |
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Chapter
1. Three pictures in quantum mechanics |
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3 | (22) |
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1.1. The Schrodinger picture |
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3 | (5) |
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1.2. The Heisenberg picture |
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8 | (3) |
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1.3. The interaction picture |
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11 | (4) |
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1.3.1. Equation of motion in the interaction picture |
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11 | (2) |
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1.3.2. A formal solution of the state vector XXX (t) by the perturbation theory |
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13 | (2) |
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1.4. The density operator |
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15 | (10) |
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1.4.1. Density operator and its general properties |
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16 | (4) |
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1.4.2. Solution of the equation of motion for the density operator |
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20 | (5) |
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Chapter
2. Two-level atom and the optical Bloch equation |
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25 | (12) |
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25 | (1) |
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2.2. Hamiltonian of a two-level atom interacting with an electromagnetic field |
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26 | (2) |
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2.3. The optical Bloch equation |
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28 | (3) |
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2.4. Description of the dynamical behavior of a two-level atom interacting with the radiation field by the density matrix |
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31 | (6) |
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2.4.1. Density matrix equation describing a two-level atom without decay |
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32 | (2) |
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2.4.2. Density matrix equation of a two-level atom with decay |
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34 | (3) |
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Chapter
3. Quantized description of radiation field |
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37 | (40) |
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3.1. Classical description of the electromagnetic field in vacuum |
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37 | (5) |
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3.2. Quantization of the radiation field |
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42 | (6) |
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3.2.1. Quantization of the electromagnetic field |
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42 | (3) |
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3.2.2. Momentum and spin of the photon |
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45 | (3) |
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3.3. State functions describing the light field |
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48 | (29) |
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3.3.1. Photon-number states |
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48 | (4) |
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3.3.2. The coherent states of light |
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52 | (8) |
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3.3.3. The phase operators and the phase states |
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60 | (12) |
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3.3.4. Chaotic states of light |
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72 | (5) |
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Chapter
4. Dicke Hamiltonian and Jaynes-Cummings Model |
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77 | (16) |
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4.1. Dicke Hamiltonian of an atom interacting with the radiation field |
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77 | (5) |
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4.2. Spontaneous emission of an excited atom |
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82 | (5) |
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4.3. The Jaynes-Cummings model |
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87 | (6) |
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Chapter
5. Quantum theory of a small system coupled to a reservoir |
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93 | (42) |
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5.1. Classical Langevin equation and Fokker-Planck equation |
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93 | (14) |
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94 | (4) |
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5.1.2. Fokker-Planck equation |
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98 | (9) |
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5.2. Master equation for a quantum harmonic oscillator and a two-level atom |
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107 | (11) |
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5.2.1. Master equation for a quantum harmonic oscillator |
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108 | (8) |
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5.2.2. Master equation for a two-level atom coupled to a bath field |
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116 | (2) |
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5.3. Characteristic function and the quasi-probability distribution for the quantum harmonic oscillator |
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118 | (17) |
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5.3.1. Normal ordering representation |
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119 | (3) |
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5.3.2. Anti-normal ordering representation |
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122 | (3) |
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5.3.3. Symmetric ordering representation |
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125 | (10) |
| PART II. The quantum properties of light |
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135 | (198) |
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Chapter
6. Coherence of light |
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135 | (25) |
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6.1. Classical coherence of light |
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135 | (10) |
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6.1.1. Temporal coherence of light |
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135 | (2) |
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6.1.2. Spatial coherence of light |
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137 | (1) |
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6.1.3. The first-order correlation function |
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138 | (4) |
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6.1.4. The higher-order correlation function |
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142 | (3) |
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6.2. Quantum theory of the coherence of light |
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145 | (15) |
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6.2.1. Quantum correlation functions |
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145 | (4) |
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6.2.2. Bunching and antibunching effects of light |
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149 | (6) |
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6.2.3. Intermode correlation property for the two-mode field |
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155 | (5) |
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Chapter
7. Squeezed states of light |
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160 | (40) |
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7.1. Squeezed states of a single-mode field |
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160 | (17) |
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7.1.1. Squeezed coherent states |
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160 | (16) |
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7.1.2. Squeezed vacuum field |
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176 | (1) |
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7.2. Squeezed states of a two-mode radiation field |
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177 | (8) |
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7.3. Higher-order Squeezing of a radiation field and the amplitude square squeezing |
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185 | (5) |
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7.3.1. Higher-order squeezing of a radiation field |
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185 | (3) |
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7.3.2. Amplitude Square Squeezing |
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188 | (1) |
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7.3.3. Independence of the different definitions of the squeezing for the radiation field |
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189 | (1) |
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7.4. Squeezing of light in the Jaynes-Cummings model |
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190 | (10) |
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Chapter
8. Resonance fluorescence |
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200 | (47) |
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8.1. Resonance fluorescence distribution of a two-level atom |
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200 | (22) |
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8.1.1. Dressed canonical transformation |
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200 | (6) |
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8.1.2. Spectral distribution of the resonance fluorescence of a two-level atom |
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206 | (3) |
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8.1.3. Linewidth of the fluorescence spectrum |
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209 | (5) |
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8.1.4. Intensity distribution of the resonance fluorescence spectrum |
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214 | (8) |
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8.2. Resonance fluorescence spectra of a three-level atom |
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222 | (14) |
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8.2.1. Hamiltonian of a three-level atom under the interaction of a bimodal field |
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222 | (2) |
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8.2.2. Resonance fluorescence spectrum of a three-level atom interacting with a strong and a weak monochromatic laser field |
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224 | (6) |
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8.2.3. Resonance fluorescence spectral distribution of a three-level atom driven by two strong laser fields |
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230 | (6) |
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8.3. Single-atom resonance fluorescence described by the density matrix theory |
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236 | (11) |
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Chapter
9. Superfluorescence |
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247 | (40) |
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9.1. Elementary features of superfluorescence |
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247 | (4) |
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9.2. Quasi-classical description of superfluorescence |
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251 | (7) |
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9.3. Quantum theoretical description of superfluorescence |
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258 | (18) |
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9.3.1. Heisenberg equation of the system |
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258 | (5) |
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9.3.2. Dicke model for superfluorescence |
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263 | (5) |
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9.3.3. Quantum statistical properties of superfluorescence |
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268 | (8) |
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9.4. Superfluorescent beats |
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276 | (11) |
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9.4.1. Basic characteristics of the superfluorescent beats |
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276 | (2) |
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9.4.2. Superfluorescent beats in the Dicke model |
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278 | (9) |
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Chapter
10. Optical Bistability |
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287 | (18) |
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10.1. Basic characteristics and the production mechanism of optical bistability |
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287 | (7) |
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10.2. Quantum description of the dispersive optical bistability |
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294 | (11) |
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10.2.1. Hamiltonian describing the optical bistability system |
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295 | (2) |
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10.2.2. Optical bistability properties of the system |
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297 | (8) |
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Chapter
11. Effects of virtual photon processes |
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305 | (28) |
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11.1. Relation between the Lamb shift of a Hydrogen atom and the virtual photon field |
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305 | (6) |
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11.2. Influence of the virtual photon field on the phase fluctuation of the radiation field |
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311 | (8) |
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11.2.1. Time evolution of the phase operator in the atom-field coupling system with the rotating-wave approximation |
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311 | (4) |
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11.2.2. Time evolution of the phase operator without the rotating-wave approximation |
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315 | (4) |
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11.3. Influences of the virtual photon processes on the squeezing of light |
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319 | (14) |
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11.3.1. Squeezing of the field in the two-photon Jaynes-Cummings model with the rotating-wave approximation |
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320 | (3) |
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11.3.2. Influences of the virtual photon processes on the squeezing of light |
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323 | (10) |
| PART III. Quantum properties of atomic behavior under the interaction of a radiation field |
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333 | (226) |
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Chapter
12. Collapses and revivals of atomic Populations |
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333 | (28) |
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12.1. Time evolution of the atomic operator of a two-level atom under the interaction of a classical electromagnetic field |
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333 | (3) |
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12.2.1. Time development of atomic operators under the interaction of the field in a number state XXX |
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337 | (1) |
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12.2.2. Periodic collapses and revivals of the atom under the interaction of a coherent field |
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338 | (9) |
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12.3. Periodic collapses and revivals of the atom in the two-photon Jaynes-Cummings model |
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347 | (4) |
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12.4. Time evolution of the atomic operators for a three-level atom interacting with a single-mode field |
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351 | (10) |
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12.4.1. Time evolution of the state vector of the system |
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351 | (10) |
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12.4.2. Periodic collapses and revivals of the atomic populations |
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354 | (7) |
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Chapter
13. Squeezing effects of the atomic operators |
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361 | (21) |
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13.1. Definition of the atomic operator squeezing |
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361 | (4) |
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13.2. Squeezing of atomic operators in the two-photon Jaynes-Cummings model |
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365 | (12) |
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13.2.1. Squeezing of atomic operators in the vacuum field |
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367 | (5) |
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13.2.2. Squeezing of atomic operators in the superposition state field |
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372 | (3) |
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13.2.3. Squeezing of atomic operators in the coherent state field |
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375 | (2) |
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13.3. Squeezing of atomic operators in the resonace flourescence system |
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377 | (5) |
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Chapter
14. Coherent trapping of the atomic population |
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382 | (19) |
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14.1. Atomic population coherent trapping and phase properties in the system of a V-configuration three-level atom interacting with a bimodal field |
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382 | (10) |
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14.1.1. Time evolution of the state vector of the system |
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383 | (2) |
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14.1.2. Time evolution of the phase operator in the atom-field coupling system |
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385 | (3) |
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14.1.3. Coherent trapping of the atomic population |
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388 | (4) |
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14.2. Coherent trapping of the atomic population for a V-configuration three-level atom driven by a classical field in a heat bath |
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392 | (9) |
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14.2.1. Time evolution of the reduced density matrix XXX of the atom |
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393 | (3) |
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14.2.2. Steady-state behavior and the coherent trapping of the atomic populations |
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396 | (5) |
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Chapter
15. Quantum characteristics of a two-atom system under the interaction of the radiation field |
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401 | (39) |
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15.1. Hamiltonian of a two-atom system with the dipole-dipole interaction |
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401 | (8) |
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15.1.1. Hamiltonian of the electric dipole-dipole interaction between two atoms |
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402 | (1) |
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15.1.2. Hamiltonian of a two-atom system with the dipole-dipole interaction induced by the fluctuations of the vacuum field |
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403 | (6) |
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15.2. Quantum characteristics of the two-atom coupling system under the interaction of a week field |
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409 | (11) |
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15.2.1. Time evolution of the atomic population inversion of a two-atom system |
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411 | (5) |
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15.2.2. Influence of the dipole-dipole interaction on the squeezing of atomic operators |
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416 | (4) |
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15.3. Periodic collapases and revivals and the coherent population trapping in the two-atom system under the interaction of a coherent field |
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420 | (20) |
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15.3.1. Periodic collapses and revivals of atomic populations in the two-atom system |
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424 | (7) |
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15.3.2. Atomic population coherent trapping in the two-atom coupling system |
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431 | (9) |
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Chapter
16. Autoionization of the atom in a laser field |
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440 | (32) |
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16.1. Autoionization of the atom in a weak laser field |
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440 | (10) |
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16.2. Autoionization of the atom under the interaction of a strong laser field |
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450 | (7) |
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16.3. Above threshold ionization of the atom in a strong laser field |
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457 | (15) |
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16.3.1. Influences of the second-order ionization processes on the low-energy photoelectron spectrum |
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464 | (2) |
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16.3.2. Higher-energy photoelectron spectrum and the peak switching effect |
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466 | (6) |
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Chapter
17. Motion of the atom in a laser field |
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472 | (49) |
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17.1. Atomic diffraction and deflection in a standing-wave field |
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472 | (18) |
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17.1.1. State function of the system of an atom interacting with a standing-wave field |
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472 | (7) |
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17.1.2. Diffraction of the atom under the interaction of a laser field |
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479 | (8) |
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17.1.3. Deflection of the atom in a standing wave field |
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487 | (3) |
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17.2. Force on an atom exerted by the radiation field |
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490 | (31) |
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17.2.1. Quasi-classical description of the radiation force |
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492 | (9) |
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17.2.2. Description of the radiative dipole force by means of the dressed state method |
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501 | (20) |
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Chapter
18. Laser cooling |
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521 | (38) |
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18.1. Decelerating the motion of atoms by use of a laser field |
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521 | (3) |
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18.2. Quantum theoretical description of the laser cooling |
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524 | (20) |
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18.2.1. Hamiltonian describing the system of a polarization laser field interacting with a quasi-two-level atom |
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524 | (5) |
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18.2.2. Time evolution of the density matrix elements of the atomic internal states |
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529 | (6) |
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18.2.3. Radiation force acting on the atom by the laser field |
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535 | (5) |
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18.2.4. Physical mechanism of the laser cooling |
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540 | (4) |
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18.3. Limited temperature of the laser cooling |
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544 | (15) |
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18.3.1. Atomic momentum diffusion in a laser field |
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544 | (8) |
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18.3.2. Equilibrium temperature of the laser cooling |
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552 | (2) |
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18.3.3. Laser cooling below the one-photon recoil energy by the velocity-selective coherent population trapping |
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554 | (5) |
| Index |
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559 | |
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