Quantum Optics

by D.F. Walls, G.J. Milburn

Overview

Quantum Optics gives a comprehensive coverage of developments in quantum optics over the past twenty years. In the early chapters the formalism of quantum optics is elucidated and the main techniques are introduced. These are applied in the later chapters to problems such as squeezed states of light, resonance fluorescence, laser theory, quantum theory of four-wave mixing, quantum non-demolition measurements, Bell's inequalities, and atom optics. Experimental results are used to illustrate the theory throughout. This yields the most comprehensive and up-to-date coverage of experiment and theory in quantum optics in any textbook.

Product Details

ISBN-13:	9783540588313
Publisher:	Springer Berlin Heidelberg
Publication date:	02/17/1995
Series:	Springer Study Edition
Edition description:	Softcover reprint of the original 1st ed. 1994
Pages:	351
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Introduction     1
Quantisation of the Electromagnetic Field     7
Field Quantisation     7
Fock or Number States     10
Coherent States     12
Squeezed States     15
Two-Photon Coherent States     18
Variance in the Electric Field     20
Multimode Squeezed States     22
Phase Properties of the Field     23
Exercises     26
References     26
Further Reading     27
Coherence Properties of the Electromagnetic Field     29
Field-Correlation Functions     29
Properties of the Correlation Functions     31
Correlation Functions and Optical Coherence     32
First-Order Optical Coherence     34
Coherent Field     37
Photon Correlation Measurements     38
Quantum Mechanical Fields     41
Squeezed State     42
Squeezed Vacuum     44
Phase-Dependent Correlation Functions     44
Photon Counting Measurements     46
Classical Theory     46
Constant Intensity     48
Fluctuating Intensity-Short-Time Limit     48
Quantum Mechanical PhotonCount Distribution     50
Coherent Light     51
Chaotic Light     51
Photo-Electron Current Fluctuations     52
Exercises     54
References     55
Further Reading     55
Representations of the Electromagnetic Field     57
Expansion in Number States     57
Expansion in Coherent States     58
P Representation     58
Wigner's Phase-Space Density     62
Q Function     65
R Representation     67
Generalized P Representations     68
Positive P Representation     71
Exercises     72
References     72
Quantum Phenomena in Simple Systems in Nonlinear Optics     73
Single-Mode Quantum Statistics     73
Degenerate Parametric Amplifier     73
Photon Statistics     75
Wigner Function     76
Two-Mode Quantum Correlations     77
Non-degenerate Parametric Amplifier     77
Squeezing     80
Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox     82
Wigner Function     83
Reduced Density Operator      84
Quantum Limits to Amplification     86
Amplitude Squeezed State with Poisson Photon Number Statistics     88
Exercises     91
References     91
Stochastic Methods     93
Master Equation     93
Equivalent c-Number Equations     99
Photon Number Representation     99
P Representation     100
Properties of Fokker-Planck Equations     102
Steady State Solutions - Potential Conditions     103
Time Dependent Solution     104
Q Representation     105
Wigner Function     107
Generalized P Representation     109
Stochastic Differential Equations     112
Use of the Positive P Representation     115
Linear Processes with Constant Diffusion     116
Two Time Correlation Functions in Quantum Markov Processes     117
Quantum Regression Theorem     118
Application to Systems with a P Representation     118
Stochastic Unravellings     119
Simulating Quantum Trajectories     123
Exercises     124
References     125
Further Reading     125
Input-Output Formulation of Optical Cavities      127
Cavity Modes     127
Linear Systems     131
Two-Sided Cavity     132
Two Time Correlation Functions     133
Spectrum of Squeezing     135
Parametric Oscillator     136
Squeezing in the Total Field     138
Fokker-Planck Equation     138
Exercises     141
References     141
Further Reading     141
Generation and Applications of Squeezed Light     143
Parametric Oscillation and Second Harmonic Generation     143
Semi-Classical Steady States and Stability Analysis     145
Parametric Oscillation     146
Second Harmonic Generation     146
Squeezing Spectrum     147
Parametric Oscillation     148
Experiments     149
Twin Beam Generation and Intensity Correlations     151
Second Harmonic Generation     156
Experiments     157
Applications of Squeezed Light     158
Interferometric Detection of Gravitational Radiation     158
Sub-Shot-Noise Phase Measurements     171
Quantum Information     173
Exercises     174
References      174
Further Reading     175
Nonlinear Quantum Dissipative Systems     177
Optical Parametric Oscillator: Complex P Function     177
Optical Parametric Oscillator: Positive P Function     181
Quantum Tunnelling Time     186
Dispersive Optical Bistability     190
Comment on the Use of the Q and Wigner Representations     192
Exercises     192
Appendix     193
Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17)     193
Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48)     194
References     195
Further Reading     195
Interaction of Radiation with Atoms     197
Quantization of the Many-Electron System     197
Interaction of a Single Two-Level Atom with a Single Mode Field     201
Spontaneous Emission from a Two-Level Atom     203
Phase Decay in a Two-Level System     204
Resonance Fluorescence     205
Exercises     210
References     210
Further Reading     211
CQED     213
Cavity QED     213
Vacuum Rabi Splitting     217
Single Photon Sources     218
Cavity QED with N Atoms     221
Circuit QED     225
Exercises     227
References     228
Further Reading     229
Quantum Theory of the Laser     231
Master Equation     231
Photon Statistics     233
Spectrum of Intensity Fluctuations     234
Laser Linewidth     237
Regularly Pumped Laser     238
Appendix: Derivation of the Single-Atom Increment     242
Exercises     245
References     245
Bells Inequalities in Quantum Optics     247
The Einstein-Podolsky-Rosen (EPR) Argument     247
Bell Inequalities and the Aspect Experiment     248
Violations of Bell's Inequalities Using a Parametric Amplifier Source     254
One-Photon Interference     259
Exercises     264
References     264
Quantum Nondemolition Measurements     267
Concept of a QND Measurement     268
Back Action Evasion     270
Criteria for a QND Measurement     270
The Beam Splitter     273
Ideal Quadrature QND Measurements     276
Experimental Realisation     277
A Photon Number QND Scheme     279
Exercises     281
References     282
Quantum Coherence and Measurement Theory     283
Quantum Coherence     283
The Effect of Dissipation     288
Experimental Observation of Coherence Decay     291
Quantum Measurement Theory     293
General Measurement Theory     294
The Pointer Basis     296
Examples of Pointer Observables     299
Model of a Measurement     299
Conditional States and Quantum Trajectories     302
Homodyne Measurement of a Cavity Field     303
Exercises     305
References     306
Quantum Information     307
Introduction     307
The Qubit     308
Entanglement     310
Quantum Key Distribution     312
Quantum Teleportation     318
Quantum Computation     324
Linear Optical Quantum Gates     327
Single Photon Sources     336
Exercises     343
References     344
Further Reading     346
Ion Traps      347
Introduction     347
Trapping and Cooling     347
Novel Quantum States     353
Trapping Multiple Ions     356
Ion Trap Quantum Information Processing     359
Exercises     362
References     363
Light Forces     365
Radiative Forces in the Semiclassical Limit     366
Mean Force for a Two-Level Atom Initially at Rest     368
Friction Force for a Moving Atom     371
Laser Standing Wave-Doppler Cooling     372
Dressed State Description of the Dipole Force     374
Atomic Diffraction by a Standing Wave     377
Optical Stern-Gerlach Effect     381
Quantum Chaos     385
Dynamical Tunnelling     387
Dynamical Localisation     389
The Effect of Spontaneous Emission     390
References     394
Further Reading     395
Bose-Einstein Condensation     397
Hamiltonian: Binary Collision Model     398
Mean-Field Theory - Gross-Pitaevskii Equation     399
Single Mode Approximation     400
Quantum State of the Condensate     401
Quantum Phase Diffusion: Collapses and Revivals of the Condensate Phase     401
Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase     405
Interference of Two Condensates Initially in Number States     405
Quantum Tunneling of a Two Component Condensate     409
Semiclassical Dynamics     411
Quantum Dynamics     414
Coherence Properties of Bose-Einstein Condensates     416
1st Order Coherence     416
Higher Order Coherence     417
Exercises     419
References     419
Further Reading     420
Index     421

Editorial Reviews

From the reviews of the second edition:

"The book contains new chapters, which cover areas of the field that were in their infancy or did not exist at all when the first edition was completed in 1994. … The second edition deserves to be intensely studied by students or young PhDs who want to pursue the research on quantum properties of light. It should also be a part of every university’s library." (Daniela Dragoman, Optics and Photonics News, November, 2008)

"This is a beautiful and self-contained textbook that unifies new and well-established basic theory and experiment. It provides the readers with … both the tools of theoretical quantum optics and clarifications on the way features of squeezed states are currently being exploited, as for prools in quantum information. … It can be definitively suggested, among the others, to all those who are willing to be safely guided into the theoretical and experimental fundamentals that place quantum optics in a central position in modern physics." (Giulio Landolfi, Zentralblatt MATH, Vol. 1163, 2009)

“Quantum optics has witnessed significant theoretical and experimental developments, which are indeed concisely and effectively surveyed in the book. It covers a broad range of topics in the field, from the fundamentals to specialized problems of modern research, through a precise, though not introductory, treatment. The book is definitely suitable to graduate students and researchers in quantum optics with a solid mathematical background. … a valuable and enjoyable tool to complete and enrich an already established knowledge in the field.” (Amalia Torre, Mathematical Reviews, Issue 2011 h)

From the Publisher