Quantum Theory of Optical Coherence: Selected Papers and Lectures

A summary of the pioneering work of Glauber in the field of optical coherence phenomena and photon statistics, this book describes the fundamental ideas of modern quantum optics and photonics in a tutorial style. It is thus not only intended as a reference for researchers in the field, but also to give graduate students an insight into the basic theories of the field. Written by the Nobel Laureate himself, the concepts described in this book have formed the basis for three further Nobel Prizes in Physics within the last decade.

Table of Contents:
1 The Quantum Theory of Optical Coherence 1 1.1 Introduction 1 1.2 Elements of Field Theory 2 1.3 Field Correlations 7 1.4 Coherence 10 1.5 Coherence and Polarization 15 Appendix 18 References 20 2 Optical Coherence and Photon Statistics 23 2.1 Introduction 23 2.1.1 Classical Theory 27 2.2 Interference Experiments 30 2.3 Introduction of Quantum Theory 35 2.4 The One-Atom Photon Detector 38 2.5 The n-Atom Photon Detector 46 2.6 Properties of the Correlation Functions 51 2.6.1 Space and Time Dependence of the Correlation Functions 54 2.7 Diffraction and Interference 56 2.7.1 Some General Remarks on Interference 58 2.7.2 First-Order Coherence 59 2.7.3 Fringe Contrast and Factorization 64 2.8 Interpretation of Intensity Interferometer Experiments 66 2.8.1 Higher Order Coherence and Photon Coincidences 67 2.8.2 Further Discussion of Higher Order Coherence 70 2.8.3 Treatment of Arbitrary Polarizations 71 2.9 Coherent and Incoherent States of the Radiation Field 75 2.9.1 Introduction 75 2.9.2 Field-Theoretical Background 77 2.9.3 Coherent States of a Single Mode 80 2.9.4 Expansion of Arbitrary States in Terms of Coherent States 86 2.9.5 Expansion of Operators in Terms of Coherent State Vectors 89 2.9.6 General Properties of the Density Operator 92 2.9.7 The P Representation of the Density Operator 94 2.9.8 The Gaussian Density Operator 100 2.9.9 Density Operators for the Field 104 2.9.10 Correlation and Coherence Properties of the Field 109 2.10 Radiation by a Predetermined Charge–Current Distribution 117 2.11 Phase-Space Distributions for the Field 121 2.11.1 The P Representation and the Moment Problem 123 2.11.2 A Positive-Definite “Phase Space Density” 124 2.11.3 Wigner’s “Phase Space Density” 127 2.12 Correlation Functions and Quasiprobability Distributions 132 2.12.1 First Order Correlation Functions for Stationary Fields 134 2.12.2 Correlation Functions for Chaotic Fields 136 2.12.3 Quasiprobability Distribution for the Field Amplitude 139 2.12.4 Quasiprobability Distribution for the Field Amplitudes at Two Space-Time Points 145 2.13 Elementary Models of Light Beams 148 2.13.1 Model for Ideal Laser Fields 153 2.13.2 Model of a Laser Field With Finite Bandwidth 156 2.14 Interference of Independent Light Beams 164 2.15 Photon Counting Experiments 170 References 181 3 Correlation Functions for Coherent Fields 183 3.1 Introduction 183 3.2 Correlation Functions and Coherence Conditions 184 3.3 Correlation Functions as Scalar Products 186 3.4 Application to Higher Order Correlation Functions 189 3.5 Fields With Positive-Definite P Functions 191 References 195 4 Density Operators for Coherent Fields 197 4.1 Introduction 197 4.2 Evaluation of the Density Operator 199 4.3 Fully Coherent Fields 205 4.4 Unique Properties of the Annihilation Operator Eigenstates 209 References 216 5 Classical Behavior of Systems of Quantum Oscillators 217 References 220 6 Quantum Theory of Parametric Amplification I 221 6.1 Introduction 221 6.2 The Coherent States and the P Representation 223 6.3 Model of the Parametric Amplifier 227 6.4 Reduced Density Operator for the A Mode 233 6.5 Initially Coherent State: P Representation for the A Mode 234 6.6 Initially Coherent State; Moments, Matrix Elements, and Explicit Representation for ρA(t) 238 6.7 Solutions for an Initially Chaotic B Mode 241 6.8 Solution for Initial n-Quantum State of A Mode; B Mode Chaotic 244 6.9 General Discussion of Amplification With B Mode Initially Chaotic 249 6.10 Discussion of P Representation: Characteristic Functions Initially Gaussian 252 6.11 Some General Properties of P(α,t) 258 Appendix 260 References 261 7 Quantum Theory of Parametric Amplification II 263 7.1 Introduction 263 7.2 The Two-Mode Characteristic Function 265 7.3 The Wigner Function 267 7.4 Decoupled Equations of Motion 271 7.5 Characteristic Functions Expressed in Terms of Decoupled Variables 273 7.6 W and P Expressed in Terms of Decoupled Variables 275 7.7 Results for Chaotic Initial States 278 7.8 Correlations of the Mode Amplitudes 283 References 286 8 Photon Statistics 287 8.1 Introduction 287 8.2 Classical Theory 288 8.3 Quantum Theory: Introduction 290 8.4 Intensity and Coincidence Measurements 293 8.5 First and Higher Order Coherence 297 8.6 The Coherent States 300 8.7 Expansions in Terms of the Coherent States 307 8.8 Characteristic Functions and Quasiprobability Densities 313 8.9 Some Examples 319 8.10 Photon Counting Distributions 322 References 329 9 Ordered Expansions in Boson Amplitude Operators 331 9.1 Introduction 331 9.2 Coherent States and Displacement Operators 333 9.3 Completeness of Displacement Operators 337 9.4 Ordered Power-Series Expansions 345 9.5 s-Ordered Power-Series Expansions 353 9.6 Integral Expansions for Operators 358 9.7 Correspondences Between Operators and Functions 366 9.8 Illustration of Operator–Function Correspondences 375 Appendix A 377 Appendix B 378 Appendix C 379 Appendix D 380 References 380 10 Density Operators and Quasiprobability Distributions 383 10.1 Introduction 383 10.2 Ordered Operator Expansions 385 10.3 The P Representation 389 10.4 Wigner Distribution 393 10.5 The Function <α|ρ|α> 399 10.6 Ensemble Averages and s Ordering 402 10.7 Examples of the General Quasiprobability Function W(α,s) 408 10.8 Analogy with Heat Diffusion 416 10.9 Time-Reversed Heat Diffusion and W(α,s) 418 10.10 Properties Common to all Quasiprobability Distributions 420 References 423 11 Coherence and Quantum Detection 425 11.1 Introduction 425 11.2 The Statistical Properties of the Electromagnetic Field 426 11.3 The Ideal Photon Detector 428 11.4 Correlation Functions and Coherence 429 11.5 Other Correlation Functions 432 11.6 The Coherent States 434 11.7 Expansions in Terms of Coherent States 437 11.8 A Few General Observations 439 11.9 The Damped Harmonic Oscillator 440 11.10 The Density Operator for the Damped Oscillator 444 11.11 Irreversibility and Damping 447 11.12 The Fokker–Planck and Bloch Equations 449 11.13 Theory of Photodetection. The Photon Counter Viewed as a Harmonic Oscillator 453 11.14 The Density Operator for the Photon Counter 459 References 462 12 Quantum Theory of Coherence 463 12.1 Introduction 463 12.2 Classical Theory 468 12.3 Quantum Theory 471 12.4 Intensity and Coincidence Measurements 474 12.5 Coherence 487 12.6 Coherent States 495 12.7 The P Representation 499 12.8 Chaotic States 514 12.9 Wavepacket Structure of Chaotic Field 521 References 530 13 The Initiation of Superfluorescence 531 13.1 Introduction 531 13.2 Basic Equations for a Simple Model 532 13.3 Onset of Superfluorescence 534 References 536 14 Amplifiers, Attenuators and Schrödingers Cat 537 14.1 Introduction: Two Paradoxes 537 14.2 A Quantum-Mechanical Attenuator: The Damped Oscillator 542 14.3 A Quantum Mechanical Amplifier 548 14.4 Specification of Photon Polarization States 558 14.5 Measuring Photon Polarizations 561 14.6 Use of the Compound Amplifier 563 14.7 Superluminal Communication? 565 14.8 Interference Experiments and Schrödinger’s Cat 569 References 575 15 The Quantum Mechanics of Trapped Wavepackets 577 15.1 Introduction 577 15.2 Equations of Motion and Their Solutions 578 15.3 The Wave Functions 581 15.4 Periodic Fields and Trapping 584 15.5 Interaction With the Radiation Field 587 15.6 Sum Rules 590 15.7 Radiative Equilibrium and Instability 592 References 594 16 Density Operators for Fermions 595 16.1 Introduction 595 16.2 Notation 597 16.3 Coherent States for Fermions 597 16.3.1 Displacement Operators 597 16.3.2 Coherent States 599 16.3.3 Intrinsic Descriptions of Fermionic States 600 16.4 Grassmann Calculus 601 16.4.1 Differentiation 601 16.4.2 Even and Odd Functions 601 16.4.3 Product Rule 602 16.4.4 Integration 602 16.4.5 Integration by Parts 603 16.4.6 Completeness of the Coherent States 604 16.4.7 Completeness of the Displacement Operators 604 16.5 Operators 605 16.5.1 The Identity Operator 605 16.5.2 The Trace 606 16.5.3 Physical States and Operators 606 16.5.4 Physical Density Operators 607 16.6 𝛿 Functions and Fourier Transforms 608 16.7 Operator Expansions 610 16.8 Characteristic Functions 612 16.8.1 The s-Ordered Characteristic Function 613 16.9 s-Ordered Expansions for Operators 614 16.10 Quasiprobability Distributions 616 16.11 Mean Values of Operators 618 16.12 P Representation 619 16.13 Correlation Functions for Fermions 620 16.14 Chaotic States of the Fermion Field 621 16.15 Correlation Functions for Chaotic Field Excitations 624 16.16 Fermion-Counting Experiments 626 16.17 Some Elementary Examples 628 16.17.1 The Vacuum State 628 16.17.2 A Physical Two-Mode Density Operator 629 References 631 Index 633