| Preface |
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xix | |
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1 Quantum theory of radiation |
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1 | (45) |
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1.1 Quantization of the free electromagnetic field |
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2 | (7) |
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1.1.1 Mode expansion of the field |
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3 | (1) |
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4 | (3) |
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1.1.3 Commutation relations between electric and magnetic field components |
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7 | (2) |
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1.2 Fock or number states |
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9 | (4) |
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13 | (3) |
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16 | (4) |
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1.5 What is light? - The photon concept |
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20 | (15) |
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1.5.1 Vacuum fluctuations and the photon concept |
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20 | (2) |
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1.5.2 Vacuum fluctuations |
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22 | (2) |
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1.5.3 Quantum beats, the quantum eraser, Bell's theorem, and more |
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24 | (1) |
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1.5.4 `Wave function for photons' |
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24 | (11) |
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1.A Equivalence between a many-particle Bose gas and a set of quantized harmonic oscillators |
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35 | (5) |
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40 | (3) |
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References and bibliography |
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43 | (3) |
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2 Coherent and squeezed states of the radiation field |
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46 | (26) |
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2.1 Radiation from a classical current |
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48 | (2) |
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2.2 The coherent state as an eigenstate of the annihilation operator and as a displaced harmonic oscillator state |
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50 | (1) |
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2.3 What is so coherent about coherent states? |
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51 | (3) |
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2.4 Some properties of coherent states |
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54 | (2) |
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2.5 Squeezed state physics |
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56 | (4) |
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2.6 Squeezed states and the uncertainty relation |
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60 | (3) |
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2.7 The squeeze operator and the squeezed coherent states |
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63 | (3) |
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2.7.1 Quadrature variance |
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65 | (1) |
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66 | (1) |
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67 | (3) |
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References and bibliography |
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70 | (2) |
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3 Quantum distribution theory and partially coherent radiation |
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72 | (25) |
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3.1 Coherent state representation |
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73 | (6) |
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3.1.1 Definition of the coherent state representation |
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75 | (2) |
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3.1.2 Examples of the coherent state representation |
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77 | (2) |
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79 | (2) |
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3.3 The Wigner-Weyl distribution |
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81 | (2) |
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3.4 Generalized representation of the density operator and connection between the P-, Q-, and W -distributions |
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83 | (3) |
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3.5 Q-representation for a squeezed coherent state |
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86 | (4) |
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3.A Verifying equations (3.1.12a, 3.1.12b) |
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90 | (2) |
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3.B c-number function correspondence for the Wigner-Weyl distribution |
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92 | (2) |
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94 | (2) |
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References and bibliography |
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96 | (1) |
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4 Field-field and photon-photon interferometry |
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97 | (48) |
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4.1 The interferometer as a cosmic probe |
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98 | (13) |
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4.1.1 Michelson interferometer and general relativity |
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98 | (3) |
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4.1.2 The Sagnac ring interferometer |
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101 | (5) |
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4.1.3 Proposed ring laser test of metric gravitation theories |
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106 | (2) |
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4.1.4 The Michelson stellar interferometer |
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108 | (2) |
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4.1.5 Hanbury-Brown-Twiss interferometer |
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110 | (1) |
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4.2 Photon detection and quantum coherence functions |
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111 | (4) |
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4.3 First-order coherence and Young-type double-source experiments |
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115 | (5) |
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4.3.1 Young's double-slit experiment |
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115 | (4) |
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4.3.2 Young's experiment with light from two atoms |
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119 | (1) |
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4.4 Second-order coherence |
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120 | (17) |
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4.4.1 The physics behind the Hanbury-Brown-Twiss effect |
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121 | (4) |
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4.4.2 Detection and measurement of squeezed states via homodyne detection |
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125 | (6) |
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4.4.3 Interference of two photons |
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131 | (3) |
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4.4.4 Photon antibunching, Poissonian, and sub-Poissonian light |
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134 | (3) |
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4.5 Photon counting and photon statistics |
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137 | (2) |
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4.A Classical and quantum descriptions of two-source interference |
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139 | (1) |
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4.B Calculation of the second-order correlation function |
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140 | (1) |
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141 | (2) |
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References and bibliography |
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143 | (2) |
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5 Atom-field interaction - semiclassical theory |
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145 | (48) |
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5.1 Atom-field interaction Hamiltonian |
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146 | (5) |
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5.1.1 Local gauge (phase) invariance and minimal-coupling Hamiltonian |
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146 | (2) |
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5.1.2 Dipole approximation and r E Hamiltonian |
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148 | (1) |
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149 | (2) |
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5.2 Interaction of a single two-level atom with a single-mode field |
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151 | (9) |
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5.2.1 Probability amplitude method |
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151 | (4) |
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5.2.2 Interaction picture |
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155 | (3) |
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5.2.3 Beyond the rotating-wave approximation |
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158 | (2) |
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5.3 Density matrix for a two-level atom |
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160 | (4) |
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5.3.1 Equation of motion for the density matrix |
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161 | (1) |
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162 | (1) |
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5.3.3 Inclusion of elastic collisions between atoms |
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163 | (1) |
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5.4 Maxwell-Schrodinger equations |
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164 | (4) |
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5.4.1 Population matrix and its equation of motion |
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165 | (1) |
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5.4.2 Maxwell's equations for slowly varying field functions |
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166 | (2) |
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5.5 Semiclassical laser theory |
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168 | (5) |
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169 | (1) |
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5.5.2 Lamb's semiclassical theory |
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169 | (4) |
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5.6 A physical picture of stimulated emission and absorption |
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173 | (1) |
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5.7 Time delay spectroscopy |
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174 | (4) |
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5.A Equivalence of the r E and the p A interaction Hamiltonians |
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178 | (5) |
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5.A.1 Form-invariant physical quantities |
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178 | (2) |
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5.A.2 Transition probabilities in a two-level atom |
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180 | (3) |
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5.B Vector model of the density matrix |
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183 | (2) |
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5.C Quasimode laser physics based on the modes of the universe |
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185 | (2) |
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187 | (3) |
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References and bibliography |
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190 | (3) |
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6 Atom-field interaction - quantum theory |
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193 | (27) |
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6.1 Atom-field interaction Hamiltonian |
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194 | (2) |
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6.2 Interaction of a single two-level atom with a single-mode field |
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196 | (10) |
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6.2.1 Probability amplitude method |
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197 | (5) |
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6.2.2 Heisenberg operator method |
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202 | (2) |
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6.2.3 Unitary time-evolution operator method |
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204 | (2) |
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6.3 Weisskopf-Wigner theory of spontaneous emission between two atomic levels |
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206 | (4) |
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210 | (3) |
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6.5 Excitation probabilities for single and double photo-excitation events |
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213 | (2) |
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215 | (2) |
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References and bibliography |
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217 | (3) |
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7 Lasing without inversion and other effects of atomic coherence and interference |
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220 | (28) |
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221 | (1) |
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7.2 Coherent trapping - dark states |
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222 | (3) |
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7.3 Electromagnetically induced transparency |
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225 | (5) |
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7.4 Lasing without inversion |
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230 | (6) |
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230 | (2) |
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7.4.2 The laser physics approach to LWI: simple treatment |
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232 | (1) |
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233 | (3) |
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7.5 Refractive index enhancement via quantum coherence |
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236 | (5) |
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7.6 Coherent trapping, lasing without inversion, and electromagnetically induced transparency via an exact solution to a simple model |
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241 | (3) |
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244 | (1) |
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References and bibliography |
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245 | (3) |
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8 Quantum theory of damping - density operator and wave function approach |
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248 | (23) |
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8.1 General reservoir theory |
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249 | (1) |
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8.2 Atomic decay by thermal and squeezed vacuum reservoirs |
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250 | (5) |
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251 | (2) |
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8.2.2 Squeezed vacuum reservoir |
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253 | (2) |
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255 | (1) |
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8.4 Fokker-Planck equation |
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256 | (4) |
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8.5 The `quantum jump' approach to damping |
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260 | (7) |
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8.5.1 Conditional density matrices and the null measurement |
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261 | (2) |
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8.5.2 The wave function Monte Carlo approach to damping |
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263 | (4) |
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267 | (2) |
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References and bibliography |
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269 | (2) |
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9 Quantum theory of damping - Heisenberg-Langevin approach |
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271 | (20) |
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9.1 Simple treatment of damping via oscillator reservoir: Markovian white noise |
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272 | (4) |
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9.2 Extended treatment of damping via atom and oscillator reservoirs: non-Markovian colored noise |
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276 | (5) |
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9.2.1 An atomic reservoir approach |
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276 | (2) |
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9.2.2 A generalized treatment of the oscillator reservoir problem |
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278 | (3) |
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9.3 Equations of motion for the field correlation functions |
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281 | (2) |
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9.4 Fluctuation-dissipation theorem and the Einstein relation |
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283 | (1) |
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9.5 Atom in a damped cavity |
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284 | (5) |
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289 | (1) |
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References and bibliography |
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290 | (1) |
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10 Resonance fluorescence |
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291 | (36) |
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10.1 Electric field operator for spontaneous emission from a single atom |
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292 | (1) |
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10.2 An introduction to the resonance fluorescence spectrum |
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293 | (5) |
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10.2.1 Weak driving field limit |
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293 | (2) |
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10.2.2 The strong field limit: sidebands appear |
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295 | (1) |
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10.2.3 The widths of the three peaks in the very strong field limit |
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296 | (2) |
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10.3 Theory of a spectrum analyzer |
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298 | (2) |
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10.4 From single-time to two-time averages: the Onsager-Lax regression theorem |
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300 | (2) |
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10.5 The complete resonance fluorescence spectrum |
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302 | (5) |
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305 | (1) |
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10.5.2 Strong field limit |
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305 | (2) |
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307 | (2) |
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10.7 Resonance fluorescence from a driven V system |
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309 | (2) |
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10.A Electric field operator in the far-zone approximation |
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311 | (5) |
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10.B The equations of motion for and exact solution of the density matrix in a dressed-state basis |
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316 | (4) |
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10.B.1 Deriving the equation of motion in the dressed-state basis |
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316 | (1) |
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10.B.2 Solving the equations of motion |
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317 | (3) |
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10.C The equations of motion for and exact solution of the density matrix in the bare-state basis |
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320 | (1) |
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10.D Power spectrum in the stationary regime |
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321 | (1) |
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10.E Derivation of Eq. (10.7.5) |
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322 | (1) |
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323 | (2) |
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References and bibliography |
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325 | (2) |
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11 Quantum theory of the laser - density operator approach |
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327 | (35) |
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11.1 Equation of motion for the density matrix |
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328 | (8) |
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11.2 Laser photon statistics |
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336 | (4) |
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11.2.1 Linear approximation (XXX = 0) |
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337 | (1) |
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11.2.2 Far above threshold (XXX) |
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338 | (1) |
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338 | (2) |
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11.3 P-representation of the laser |
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340 | (1) |
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341 | (5) |
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11.4.1 Phase diffusion model |
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342 | (3) |
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11.4.2 Fokker-Planck equation and laser linewidth |
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345 | (1) |
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11.5 Off-diagonal elements and laser linewidth |
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346 | (3) |
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11.6 Analogy between the laser threshold and a second-order phase transition |
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349 | (3) |
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11.A Solution of the equations for the density matrix elements |
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352 | (2) |
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11.B An exact solution for the P-representation of the laser |
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354 | (4) |
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358 | (2) |
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References and bibliography |
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360 | (2) |
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12 Quantum theory of the laser - Heisenberg-Langevin approach |
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362 | (21) |
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12.1 A simple Langevin treatment of the laser linewidth including atomic memory effects |
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362 | (5) |
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12.2 Quantum Langevin equations |
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367 | (6) |
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12.3 c-number Langevin equations |
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373 | (3) |
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12.4 Photon statistics and laser linewidth |
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376 | (4) |
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380 | (1) |
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References and bibliography |
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381 | (2) |
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13 Theory of the micromaser |
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383 | (19) |
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13.1 Equation of motion for the field density matrix |
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384 | (2) |
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13.2 Steady-state photon statistics |
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386 | (3) |
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13.3 Preparation of number state in a high-Q micromaser |
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389 | (7) |
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390 | (3) |
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393 | (3) |
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13.4 Linewidth of a micromaser |
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396 | (2) |
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398 | (2) |
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References and bibliography |
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400 | (2) |
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14 Correlated emission laser: concept, theory, and analysis |
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402 | (40) |
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14.1 Correlated spontaneous emission laser concept |
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403 | (2) |
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14.2 Hanle effect correlated emission laser via density matrix analysis |
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405 | (8) |
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14.3 Quantum beat laser via pictorial treatment |
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413 | (5) |
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418 | (5) |
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14.5 Quantum phase and amplitude fluctuations |
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423 | (3) |
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14.6 Two-photon correlated emission laser |
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426 | (7) |
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426 | (4) |
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14.6.2 Heuristic account of a two-photon CEL |
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430 | (3) |
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14.A Spontaneous emission noise in the quantum beat laser |
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433 | (4) |
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437 | (3) |
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References and bibliography |
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440 | (2) |
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15 Phase sensitivity in quantum optical systems: applications |
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442 | (18) |
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442 | (4) |
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15.2 Linear amplification process: general description |
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446 | (2) |
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15.3 Phase-insensitive amplification in a two-level system |
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448 | (2) |
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15.4 Phase-sensitive amplification via the two-photon CEL: noise-free amplification |
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450 | (2) |
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15.5 Laser with an injected squeezed vacuum |
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452 | (2) |
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15.A Analysis of the CEL gyro with reinjection |
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454 | (3) |
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457 | (1) |
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References and bibliography |
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458 | (2) |
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16 Squeezing via nonlinear optical processes |
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460 | (27) |
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16.1 Degenerate parametric amplification |
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460 | (3) |
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16.2 Squeezing in an optical parametric oscillator |
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463 | (4) |
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16.3 Squeezing in the output of a cavity field |
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467 | (4) |
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471 | (5) |
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16.4.1 Amplification and oscillation in four-wave mixing |
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471 | (4) |
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16.4.2 Squeezing in four-wave mixing |
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475 | (1) |
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16.A Effect of pump phase fluctuations on squeezing in degenerate parametric amplification |
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476 | (4) |
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16.B Quantized field treatment of input-output formalism leading to Eq. (16.3.4) |
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480 | (2) |
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482 | (2) |
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References and bibliography |
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484 | (3) |
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487 | (20) |
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17.1 Mechanical effects of light |
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488 | (6) |
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488 | (1) |
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489 | (1) |
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17.1.3 Atomic diffraction |
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490 | (3) |
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17.1.4 Semiclassical gradient force |
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493 | (1) |
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17.2 Atomic interferometry |
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494 | (4) |
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17.2.1 Atomic Mach-Zehnder interferometer |
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494 | (2) |
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496 | (2) |
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17.3 Quantum noise in an atomic interferometer |
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498 | (1) |
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17.4 Limits to laser cooling |
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499 | (4) |
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499 | (2) |
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17.4.2 Velocity selective coherent population trapping |
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501 | (2) |
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503 | (1) |
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References and bibliography |
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504 | (3) |
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18 The EPR paradox, hidden variables, and Bell's theorem |
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507 | (34) |
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508 | (5) |
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513 | (2) |
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18.3 Quantum calculation of the correlations in Bell's theorem |
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515 | (5) |
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18.4 Hidden variables from a quantum optical perspective |
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520 | (9) |
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18.5 Bell's theorem without inequalities: Greenberger-Horne-Zeilinger (GHZ) equality |
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529 | (2) |
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18.6 Quantum cryptography |
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531 | (2) |
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18.6.1 Bennett-Brassard protocol |
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531 | (1) |
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18.6.2 Quantum cryptography based on Bell's theorem |
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532 | (1) |
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18.A Quantum distribution function for a single spin-up particle |
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533 | (1) |
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18.B Quantum distribution function for two particles |
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534 | (2) |
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536 | (3) |
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References and bibliography |
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539 | (2) |
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19 Quantum nondemolition measurements |
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541 | (20) |
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19.1 Conditions for QND measurements |
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542 | (1) |
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19.2 QND measurement of the photon number via the optical Kerr effect |
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543 | (4) |
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19.3 QND measurement of the photon number by dispersive atom-field coupling |
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547 | (7) |
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19.4 QND measurement in optical parametric processes |
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554 | (4) |
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558 | (2) |
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References and bibliography |
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560 | (1) |
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20 Quantum optical tests of complementarity |
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561 | (21) |
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20.1 A micromaser which-path detector |
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564 | (2) |
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20.2 The resonant interaction of atoms with a microwave field and its effect on atomic center-of-mass motion |
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566 | (2) |
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568 | (5) |
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20.4 Quantum optical Ramsey fringes |
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573 | (3) |
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20.A Effect of recoil in a micromaser which-path detector |
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576 | (3) |
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579 | (1) |
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References and bibliography |
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580 | (2) |
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21 Two-photon interferometry, the quantum measurement problem, and more |
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582 | (42) |
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21.1 The field-field correlation function of light scattered from two atoms |
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582 | (5) |
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21.1.1 Correlation function G(1)(r,t) generated by scattering from two excited atoms |
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585 | (1) |
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21.1.2 Excitation by laser light |
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585 | (1) |
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21.1.3 Using three atomic levels as a which-path flag |
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586 | (1) |
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21.2 The field-field and photon-photon correlations of light scattered from two multi-level atoms: quantum eraser |
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587 | (5) |
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21.2.1 Alternative photon basis |
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590 | (2) |
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21.3 Bell's inequality experiments via two-photon correlations |
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592 | (3) |
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21.4 Two-photon cascade interferometry |
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595 | (5) |
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21.4.1 Two-photon correlations produced by atomic cascade emission |
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595 | (2) |
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21.4.2 Franson-Chiao interferometry |
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597 | (3) |
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21.5 Two-particle interferometry via nonlinear down-conversion and momentum selected photon pairs |
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600 | (7) |
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21.5.1 Two-site down-conversion interferometry |
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601 | (6) |
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21.6 A vacuum-fluctuation picture of the ZWM experiment |
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607 | (3) |
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21.7 High-resolution spectroscopy via two-photon cascade interferometry |
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610 | (4) |
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21.A Scattering from two atoms via an operator approach |
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614 | (2) |
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21.B Calculation of the two-photon correlation function in atomic cascade emission |
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616 | (2) |
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21.C Calculation of the joint count probability in Franson-Chiao interferometry |
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618 | (3) |
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621 | (1) |
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References and bibliography |
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622 | (2) |
| Index |
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624 | |
