Preface |
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xi | |
Acknowledgments |
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xv | |
1 Introduction |
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1 | (16) |
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3 | (6) |
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3 | (1) |
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4 | (1) |
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1.1.3 Classical electrodynamics and relativity |
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5 | (2) |
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1.1.4 Quantum mechanics and quantum electrodynamics |
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7 | (2) |
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1.2 A brief history of cavity QED |
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9 | (2) |
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11 | (3) |
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1.4 How to read this book |
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14 | (3) |
2 Fiat Lux! |
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17 | (52) |
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2.1 How to quantize a theory |
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18 | (6) |
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2.2 Why the radiation field is special |
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24 | (3) |
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27 | (12) |
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29 | (5) |
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2.3.2 Confinement is the key |
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34 | (5) |
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2.4 Canonical quantization of the radiation field |
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39 | (8) |
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2.4.1 Quantization in a cavity |
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39 | (4) |
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2.4.2 Quantization in free space |
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43 | (4) |
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47 | (16) |
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2.5.1 Zero-point potential energy |
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48 | (6) |
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2.5.2 Maxwell stress tensor |
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54 | (8) |
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2.5.3 The vacuum catastrophe |
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62 | (1) |
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63 | (2) |
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65 | (4) |
3 The photon's wavefunction |
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69 | (44) |
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3.1 Position in relativistic quantum mechanics |
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71 | (3) |
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3.2 Extreme quantum theory of light with a twist |
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74 | (15) |
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3.3 The configuration space problem |
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89 | (1) |
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3.4 Back to vector notation |
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90 | (4) |
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3.5 The limit of vanishing rest mass |
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94 | (5) |
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99 | (7) |
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106 | (3) |
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109 | (4) |
4 A box of photons |
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113 | (32) |
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113 | (11) |
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114 | (4) |
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118 | (3) |
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4.1.3 The diagonal coherent-state representation |
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121 | (3) |
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124 | (18) |
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4.2.1 The squeezing operator |
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125 | (5) |
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4.2.2 Generating squeezed states |
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130 | (3) |
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4.2.3 Geometrical picture |
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133 | (6) |
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139 | (3) |
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142 | (1) |
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143 | (2) |
5 Let matter be! |
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145 | (20) |
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5.1 A single point dipole |
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146 | (8) |
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5.2 An arbitrary charge distribution |
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154 | (7) |
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5.3 Matter radiation coupling and gauge invariance |
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161 | (2) |
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163 | (2) |
6 Spontaneous emission |
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165 | (18) |
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6.1 Emission in free space |
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166 | (10) |
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176 | (6) |
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182 | (1) |
7 Macroscopic QED |
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183 | (30) |
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185 | (6) |
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7.2 Polariton-photon dressed excitations |
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191 | (2) |
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7.3 Quantum noise of matter and macroscopic averages |
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193 | (3) |
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7.4 How a macroscopic description is possible |
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196 | (2) |
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7.5 The Kramers-Kronig dispersion relation |
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198 | (1) |
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7.6 Including absorption in the dielectric JCM |
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198 | (4) |
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7.7 Dielectric permittivity |
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202 | (3) |
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7.8 Huttner-Barnett theory |
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205 | (5) |
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7.8.1 The matter Hamiltonian |
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206 | (2) |
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7.8.2 Diagonalization of the total Hamiltonian |
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208 | (2) |
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210 | (1) |
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211 | (2) |
8 The maser the laser, and their cavity QED cousins |
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213 | (42) |
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214 | (6) |
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220 | (11) |
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8.2.1 Einstein's approach to Brownian motion |
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221 | (1) |
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8.2.2 Langevin 's approach to Brownian motion |
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222 | (1) |
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8.2.3 The modern form of Langevin 's equation |
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223 | (2) |
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8.2.4 Ito's and Stratonovich's stochastic calculus |
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225 | (6) |
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8.3 Rate equations with noise |
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231 | (4) |
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235 | (3) |
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8.5 The single-atom maser |
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238 | (7) |
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8.6 The thresholdless laser |
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245 | (5) |
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8.7 The one-and-the-same atom laser |
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250 | (1) |
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251 | (2) |
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253 | (2) |
9 Open cavities |
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255 | (28) |
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9.1 The Gardiner-Collett Hamiltonian |
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258 | (11) |
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9.2 The radiation condition |
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269 | (1) |
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270 | (1) |
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9.4 Completeness in general |
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271 | (5) |
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9.4.1 Whittaker's scalar potentials |
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272 | (2) |
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9.4.2 General formulation of the problem |
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274 | (2) |
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276 | (1) |
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277 | (6) |
Appendix A Perfect cavity modes |
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283 | (8) |
Appendix B Perfect cavity boundary conditions |
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291 | (2) |
Appendix C Quaternions and special relativity |
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293 | (18) |
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C.1 What are quaternions? |
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295 | (5) |
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300 | (4) |
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C.3 Biquaternions and Lorentz transformations |
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304 | (7) |
Appendix D The Baker-Hausdorff formula |
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311 | (2) |
Appendix E Vectors and vector identities |
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313 | (8) |
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E.1 Relation between vector products and determinants |
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314 | (1) |
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E.2 Vector products and the Levy-Civita tensor |
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315 | (1) |
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E.3 The product of two Levy-Civita tensors as a determinant |
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316 | (1) |
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E.4 The vector product of three vectors |
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316 | (1) |
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E.5 Vectorial expressions involving del |
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317 | (1) |
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E.6 Some useful integral theorems |
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318 | (3) |
Appendix F The Good, the Bad, and the Ugly |
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321 | (14) |
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322 | (9) |
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F1.1 The rectangular barrier |
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323 | (1) |
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324 | (1) |
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F1.3 The Lorentzian representation and the principal part |
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324 | (2) |
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326 | (1) |
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F1.5 The Laplacian of 1/r |
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327 | (1) |
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327 | (1) |
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F1.7 A general rule to find representations |
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328 | (3) |
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F2 Product of two principal parts |
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331 | (1) |
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F3 Discontinuous functions |
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331 | (4) |
References |
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335 | (46) |
Index |
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381 | |