Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence

by Miguel Orszag

Overview

Quantum Optics gives a very broad coverage of basic laser-related phenomena that allow scientist and engineers to carry out research in quantum optics and laser physics. It covers quantization of the electromagnetic field, quantum theory of coherence, atom-field interaction models, resonance fluorescence, quantum theory of damping, laser theory using both the master equation and the Langevin theory, the correlated emission laser, input-output theory with applications to non-linear optics, quantum trajectories, quantum non-demolition measurements and generation of non-classical vibrational states of ions in a Paul trap. In this second edition, there is an enlarged chapter on decoherence, as well as additional material dealing with elements of quantum computation, entanglement of pure and mixed states as well as a chapter on quantum copying and processors.

These topics are presented in a unified and didactic manner. The presentation of the book is clear and pedagogical; it balances the theoretical aspect of quantum optics and quantum information theory with recent relevant experiments.

Product Details

ISBN-13:	9783031548536
Publisher:	Springer-Verlag New York, LLC
Publication date:	06/29/2024
Sold by:	Barnes & Noble
Format:	eBook
File size:	44 MB
Note:	This product may take a few minutes to download.

About the Author

Prof. Dr. Miguel Orszag
Universidad Mayor
Centro Multidisciplinario de Fisica
Santiago, Chile

Table of Contents

Einstein's Theory of Atom-Radiation Interaction     1
The A and B Coefficients     1
Thermal Equilibrium     3
Photon Distribution and Fluctuations     4
Light Beam Incident on Atoms     5
An Elementary Laser Theory     5
Threshold and Population Inversion     6
Steady State     7
Linear Stability Analysis     8
References     9
Further Reading     9
Atom-Field Interaction: Semiclassical Approach     11
Broad-Band Radiation Spectrum     14
Rabi Oscillations     15
Bloch's Equations     16
Decay to an Unobserved Level     17
Decay Between Levels     18
Optical Nutation     18
References     19
Further Reading     19
Quantization of the Electromagnetic Field     21
Fock States     24
Density of Modes     25
Commutation Relations     26
Reference     28
Further Reading     28
States of the Electromagnetic Field I     31
Further Properties     32
Coherent States are Minimum Uncertainty States     32
Coherent States are not Orthogonal     32
Coherent States are Overcomplete     33
The Displacement Operator     33
Photon Statistics     34
Coordinate Representation     35
Mixed State: Thermal Radiation     35
References     39
Further Reading     39
States of the Electromagnetic Field II     41
Squeezed States: General Properties and Detection     41
The Squeeze Operator and the Squeezed State     43
The Squeezed State is an Eigenstate of A     44
Calculation of Moments with Squeezed States     44
Quadrature Fluctuations     45
Photon Statistics     46
Multimode Squeezed States     47
Detection of Squeezed States     47
Ordinary Homodyne Detection     48
Balanced Homodyne Detection     50
Heterodyne Detection     50
References     51
Quantum Theory of Coherence     53
One-Atom Detector     54
The n-Atom Detector     57
General Properties of the Correlation Functions     59
Young's Interference and First-Order Correlation     60
Second-Order Correlations: Photon Bunching and Antibunching     62
Classical Second-Order Coherence     63
Quantum Theory of Second-Order Coherence     65
Photon Counting     67
Some Simple Examples     70
Quantum Mechanical Photon Count Distribution     71
Particular Examples     72
References     72
Further Reading     72
Phase Space Description     73
Q-Representation: Antinormal Ordering     73
Normalization     73
Average of Antinormally Ordered Products     74
Some Examples     74
The Density Operator in Terms of the Function Q     75
Characteristic Function     76
P Representation: Normal Ordering     76
Normalization     76
Averages of Normally Ordered Products     77
Some Interesting Properties     77
Some Examples     77
The Wigner Distribution: Symmetric Ordering     79
Moments     80
References     82
Further Reading     82
Atom-Field Interaction     83
Atom-Field Hamiltonian and the Dipole Approximation     83
A Two-Level Atom Interacting with a Single Field Mode      85
The Dressed State Picture: Quantum Rabi Oscillations     88
Collapse and Revivals     91
References     94
Further Reading     94
System-Reservoir Interactions     97
Quantum Theory of Damping     97
General Properties     100
Expectation Values of Relevant Physical Quantities     101
Time Evolution of the Density Matrix Elements     102
The Glauber-Sudarshan Representation, and the Fokker-Planck Equation     105
Time-Dependent Solution: The Method of the Eigenfunctions     106
General Solution     107
Langevin's Equations     108
Calculation of the Correlation Function [left angle bracket]F(t')F(t")[characters not reproducible right angle bracket subscript B]     109
Differential Equation for the Photon Number     109
Other Master Equations     110
Two-Level Atom in a Thermal Bath     110
Damped Harmonic Oscillator in a Squeezed Bath     111
Application: Spontaneous Decay in a Squeezed Vaccum     114
References     116
Further Reading     117
Resonance Fluorescence     119
Background     119
Heisenberg's Equations      120
Spectral Density, and the Wiener-Khinchine Theorem     124
Emission Spectra from Strongly Driven Two-Level Atoms     126
Intensity Correlations     129
References     133
Further Reading     134
Quantum Laser Theory: Master Equation Approach     135
Heuristic Discussion of Injection Statistics     136
Master Equation for Generalized Pump Satistics     137
The Quantum Theory of the Laser: Random Injection (p = 0)     139
Photon Statistics     140
The Fokker-Planck Equation: Laser Linewidth     143
Alternative Derivation of the Laser Linewidth     144
Quantum Theory of the Micromaser: Random injection (p = 0)     146
Generalities     146
The Micromaser     147
Trapping States     149
Quantum Theory of the Laser and the Micromaser with Pump Statistics (p [not equal] 0)     153
References     157
Further Reading     157
Quantum Laser Theory: Langevin Approach     159
Quantum Langevin Equations     159
The Generalized Einstein's Relations     160
The Atomic Noise Moments     161
C-Number Langevin Equations     165
Adiabatic Approximation     166
Phase and Intensity Fluctuations     167
Discussion     168
References     170
Further Reading     171
Quantum Noise Reduction 1     173
Correlated Emission Laser Systems     175
The Quantum Beat Laser     175
Other CEL Systems     181
References     182
Further Reading     182
Quantum Noise Reduction 2     185
Introduction to Non-Linear Optics     185
Multiple-Photon Transitions     185
Parametric Processes Without Losses     189
The Input-Output Theory     191
The Degenerate Parametric Oscillator     195
Experimental Results     198
References     201
Quantum Phase     203
The Dirac Phase     203
The Louisell Phase     204
The Susskind-Glogower Phase     204
The Pegg-Barnett Phase     208
Applications     211
Phase Fluctuations in a Laser     213
References     217
Further Reading     217
Quantum Trajectories     219
Montecarlo Wavefunction Method      220
The Montecarlo Method is Equivalent, on the Average, to the Master Equation     221
The Stochastic Schrodinger Equation     223
Stochastic Schrodinger Equations and Dissipative Systems     225
Simulation of a Monte Carlo SSE     227
Simulation of the Homodyne SSDE     232
Numerical Results and Localization     236
Quantum Jumps Evolution     236
Diffusion-like Evolution     237
Analytical Proof of Localization     239
Conclusions     242
References     244
Further Reading     245
Atom Optics     247
Optical Elements     247
Atomic Diffraction from an Optical Standing Wave     248
Theory     249
Particular Cases     252
Atomic Focusing     255
The Model     255
Initial Conditions and Solution     257
Quantum and Classical Foci     258
Thin Versus Thick Lenses     258
The Quantum Focal Curve     259
Aberrations     261
References     262
Measurements, Quantum Limits and All That     263
Quantum Standard Limit     263
Quantum Standard Limit for a Free Particle     263
Standard Quantum Limit for an Oscillator     264
Thermal Effects     265
Quantum Non-Demolition (QND) Measurements     266
The Free System     266
Monitoring a Classical Force     268
Effect of the Measuring Apparatus or Probe     269
QND Measurement of the Number of Photons in a Cavity     270
The Model     270
The System-Probe Interaction     271
Measuring the Atomic Phase with Ramsey Fields     272
QND Measurement of the Photon Number     275
Quantum Theory of Continuous Photodetection Process     278
Introduction     278
Continuous Measurement in a Two-Mode System: Phase Narrowing     280
References     284
Further Reading     285
Trapped Ions     287
Paul Trap     287
General Properties     287
Stability Analysis     290
Trapped Ions     294
Introduction     294
The Model and Effective Hamiltonian     294
The Lamb-Dicke Expansion and Raman Cooling     299
The Dynamical Evolution     300
QND Measurements of Vibrational States      303
Generation of Non-Classical Vibrational States     305
References     309
Further Reading     309
Decoherence     311
Dynamics of the Correlations     314
How Long Does It Take to Decohere?     315
Decoherence Free Subspaces     320
Simple Example: Collective dephasing     320
General Treatment     322
Condition for DFS: Hamiltonian Approach     323
Condition for DFS: Lindblad Approach     323
Example: N Spins in Boson Bath     326
References     327
Further Reading     328
Quantum Bits, Entanglement and Applications     329
Qubits and Quantum Gates     329
Entanglement     333
Pure States     333
Mixed states     339
Bell Inequalities     341
Quantum Teleportation     344
References     347
Quantum Cloning and Processing     349
The No-Cloning Theorem     349
The Universal Quantum Copying Machine (UQCM)     350
Quantum Copying Machine Implemented by a Circuit     351
Preparation Stage     352
Copying Stage and Output      353
Output States     355
Summary and Discussion     356
Quantum Processors     357
Introduction     357
One Qubit Stochastic Processor     359
References     361
Operator Relations     363
Theorem 1     363
Theorem 2: The Baker-Campbell-Haussdorf Relation     364
Theorem 3: Similarity Transformation     365
Reference     366
The Method of Characteristics     367
Reference     369
Proof     371
References     372
Stochastic Processes in a Nutshell     373
Introduction     373
Probability Concepts     374
Stochastic Processes     375
The Chapman-Kolmogorov Equation     375
The Fokker-Planck Equation     378
The Wiener Process     379
General Properties of the Fokker-Planck Equation     381
Steady-State Solution     381
Stochastic Differential Equations     382
Introduction     382
Ito Versus Stratonovich     384
Ito's Formula     386
Approximate Methods     388
References      391
Derivation of the Homodyne Stochastic Schrodinger Differential Equation     393
Fluctuations     397
The No-Cloning Theorem     399
Reference     399
The Universal Quantum Cloning Machine     401
Reference     402
Hints to Solve the Problems     403
Index     409

Editorial Reviews

The third edition of this book contains extensive and thorough coverage of basic laser-related phenomena including quantization of the electromagnetic field, quantum theory of coherence, laser theory using both the master equation and the Langevin theory, and generation of non-classical vibrational states of ions in a Paul trap. … it will be of interest to a great variety of readers, including graduate students, scientists and engineers. … It is a valuable addition to textbook literature in quantum optics.” (Christian Brosseau, Optics & Photonics News, osa-opn-org, March, 2017)

From the Publisher