Statistical Methods in Quantum Optics 2 (eBook)

Howard Carmichael earned a PhD from the University of Waikato in 1977. He joined the faculty of the University of Arkansas in 1983 and moved to the University of Oregon in 1989, where he was Professor of Physics from 1991 to 2001. He is currently a member of the Physics Department at the University of Auckland where he holds the Dan Walls Chair in Theoretical Physics. He is a Fellow of the Optical Society of America, the American Physical Society, and the Royal Society of New Zealand. Professor Carmichael was the recipient in 2003 of the Max Born Award of the Optical Society of America.

Preface 6
Contents 10
9 The Degenerate Parametric Oscillator I: Squeezed States 15
9.1 Introduction 15
9.2 Degenerate Parametric Amplification and Squeezed States 18
9.3 The Spectrum of Squeezing 45
10 The Degenerate Parametric Oscillator II: Phase- Space Analysis in the Small- Noise Limit 74
10.1 Phase-Space Formalism for the Degenerate Parametric Oscillator 74
10.2 Squeezing: Quantum Fluctuations in the Small-Noise Limit 84
11 The Positive P Representation 108
11.1 The Positive P Representation 109
11.2 Miscellaneous Topics 130
12 The Degenerate Parametric Oscillator III: Phase- Space Analysis Outside the Small- Noise Limit 146
12.1 The Degenerate Parametric Oscillator with Adiabatic Elimination of the Pump 147
12.2 Difficulties with the Positive P Representation 194
13 Cavity QED I: Simple Calculations 207
13.1 System Size and Coupling Strength 208
13.2 Cavity QED in the Perturbative Limit 210
13.3 Nonperturbative Cavity QED 243
14 Many Atoms in a Cavity: Macroscopic Theory 259
14.1 Optical Bistability: Steady-State Transmission of a Nonlinear Fabry– Perot 259
14.2 The Mean-Field Limit for a Homogeneously Broadened Two-Level Medium 265
14.3 Relationship Between Macroscopic and Microscopic Variables 283
14.4 Cavity QED with Many Atoms 287
15 Many Atoms in a Cavity II: Quantum Fluctuations in the Small- Noise Limit 297
15.1 Microscopic Model 298
15.2 Linear Theory of Quantum Fluctuations 310
16 Cavity QED II: Quantum Fluctuations 346
16.1 Density Matrix Expansion for the Weak- Excitation Limit 346
16.2 Spatial Effects 371
16.3 Beyond Classical Trajectories plus Fuzz”: Spontaneous Dressed- State Polarization 379
17 Quantum Trajectories I: Background and Interpretation 412
17.1 Density Operators and Scattering Records 414
17.2 Generalizing the Bohr–Einstein Quantum Jump 421
17.3 Miscellaneous Observations 437
18 Quantum Trajectories II: The Degenerate Parametric Oscillator 447
18.1 Scattering Records and Photoelectron Counting 447
18.2 Unraveling the Density Operator 457
18.3 Physical Interpretation 476
19 Quantum Trajectories III: More Examples 488
19.1 Photon Scattering in the Weak-Excitation Limit 488
19.2 Unraveling the Density Operator: Cascaded Systems 493
19.3 Optical Spectra 508
References 524
Index 536