Quantum Imaging Book

Quantum Imaging with Continuous Variables   Luigi A. Lugiato   Alessandra Gatti   Enrico Brambilla     1
Introduction     1
The Concepts of Squeezing and of Entanglement with Continuous Variables, and Their Intrinsic Connection     2
Prototype Model I     2
Prototype Model II     3
Intrinsic Relation Between Squeezing and Entanglement     5
Spatially Multimode Parametric Down-Conversion: Some Topics in Quantum Imaging     7
Spatially Multimode Versus Single-Mode Squeezing: Optical Parametric Down-Conversion of Type-I     7
Near-Field/Far-Field Duality in Type-I OPAs     8
Detection of Weak Amplitude or Phase Objects Beyond the Standard Quantum Limit     11
Image Amplification by Parametric Down-Conversion (Type-I)     12
References     14
Spatial Entanglement in Optical Parametric Down-Conversion   Alessandra Gatti   Enrico Brambilla   Ottavia Jedrkiewicz   Luigi A. Lugiato     17
Introduction     17
Simultaneous Near-Field and Far-Field Spatial Quantum Correlation in the High-Gain Regime of Type-II Parametric Down-Conversion     17
Propagation Equations for the Signal-Idler Fields and Input-Output Relations     17
Near- and Far-FieldCorrelations in the Stationary and Plane-Wave Pump Approximation     22
Near- and Far-Field Correlations: Numerical Results in the General Case     25
Far-Field Correlations     25
Near-Field Correlations     26
Detection of Sub-Shot-Noise Spatial Correlations in High-Gain Parametric Down-Conversion     28
Detection of the Spatial Features of the Far-Field PDC Radiation by Means of the CCD     29
Experimental Set-Up for Spatial-Correlations Measurements     30
Detection of Quantum Spatial Correlations: Spatial Analogue of Photon Antibunching in Time     33
Multiphoton, Multimode Polarization Entanglement in Parametric Down-Conversion     38
References     43
Quantum Imaging in the Continuous-Wave Regime Using Degenerate Optical Cavities   Agnes Maitre   Nicolas Treps   Claude Fabre     47
Introduction     47
Classical Imaging Properties of Degenerate Optical Cavities     47
Introduction     47
Cavity Round-Trip Transform     48
Image Transmission Through an Optical Cavity     50
Theory of Optical Parametric Oscillation in a Degenerate Cavity     52
Classical Behavior     52
Quantum Properties     54
Experimental Results      57
Classical Effects: Observation of Optical Patterns     58
Observation of Quantum Correlations in Images     59
Conclusion     63
References     63
Quantum Imaging by Synthesis of Multimode Quantum Light   Nicolas Treps   Hans A. Bachor   Ping Koy Lam   Claude Fabre     67
Introduction     67
Quantum Noise in an Arraylike Detection     68
Implementing a Sub-Shot-Noise Array Detection     70
The Quantum Laser Pointer     71
Optical Read-Out     73
Measuring a Signal in an Optimal Way     76
Conclusion     77
References     78
Ghost Imaging   Alessandra Gatti   Enrico Brambilla   Morten Bache   Luigi A. Lugiato     79
Introduction     79
General Theory of Ghost Imaging with Entangled Beams     81
Specific Imaging Schemes     83
Wave-Particle Aspect     85
Spatial Average in Ghost Diffraction: Increase of Spatial Bandwidth and of Speed in Retrieval     87
Ghost Imaging with Homodyne Detection     88
Debate: Is Quantum Entanglement Really Necessary for Ghost Imaging?     90
Ghost Imaging by Split Thermallike Beams: Theory [15-17]     92
Analogy Between Thermal and Entangled Beams in Ghost Imaging [15-17]     93
Resolution Aspects     95
Relations with the Classic Hanburry-Brown and Twiss Correlation Technique [37]     95
Correlation Aspects     96
Visibility Aspects     98
Some Historical Considerations     100
Rule-of-Thumb Comparison Between Entangled and "Thermal" Ghost Imaging     100
Ghost Imaging with Split Thermal Beams: Experiment     101
High-Resolution Ghost Imaging [23]     102
The Ghost Diffraction Experiment: Complementarity Between Coherence and Correlation [24]     107
References     110
Quantum Limits of Optical Super-Resolution   Mikhail I. Kolobov     113
Super-Resolution in Classical Optics     113
Quantum Theory of Super-Resolution     115
Quantum Theory of Optical Imaging     115
Quantum Theory of Optical Fourier Microscopy     119
Quantum Limits in Reconstruction of Optical Objects     121
Reconstruction of Classical Noise-Free Objects     121
Reconstruction of Objects with Quantum Fluctuations     126
Point-Spread Function for Super-Resolving Reconstruction of Objects      128
Squeezed-Light Source for Microscopy with Super-Resolution     132
References     138
Noiseless Amplification of Optical Images   Mikhail I. Kolobov   Eric Lantz     141
Introduction     141
Traveling-Wave Scheme for Amplification of Images     142
Optimum Phase Matching for Parametric Amplification     145
Quantum Fluctuations in the Amplified Image and Conditions for Noiseless Amplification     149
Experimental Demonstration of Temporally Noiseless Image Amplification     155
Experiment on Spatially Noiseless Amplification of Images     158
References     164
Optical Image Processing in Second-Harmonic Generation   Pierre Scotto   Pere Colet   Adrian Jacobo   Maxi San Miguel     167
Introduction     167
Image Processing in Second-Harmonic Generation at a Classical Level     168
Frequency Up-Conversion of an Image     171
Contrast Enhancement and Contour Recognition     172
Noise Filtering Properties     174
Quantum Image Processing in Type-I Second-Harmonic Generation     175
Field-Operator Dynamics     176
Quantum Image Processing     181
Quantum Image Processing in Type-II Second-Harmonic Generation     188
Propagation Equations     189
Linearly y-Polarized Pump: Frequency Addition Regime     192
45[Characters not reproducible]-Linearly Polarized Pump: Noiseless Up-Conversion and Amplification     193
References     199
Transverse Distribution of Quantum Fluctuations in Free-Space Spatial Solitons   Eric Lantz   Nicolas Treys   Claude Fabre     201
Introduction     201
General Method     202
Propagation Equations for the Fluctuations     202
Green's Function Approach     203
Correlations Between the Photocurrents     204
Spatial Solitons: Mean Values     205
X[superscript (3)] Scalar Spatial Soliton     205
X[superscript (3)] Vector Spatial Soliton     206
X[superscript (2)] Spatial Soliton     206
Squeezing on the Total Beam     208
X[superscript (3)] Scalar Spatial Soliton     208
X[superscript (3)] Vector Soliton: Total Beam Squeezing and Correlation Between Polarizations     208
X[superscript (3)] Spatial Solitons     210
Local Quantum Fluctuations     211
X[superscript (3)] Scalar Spatial Soliton     211
Intensity Squeezing by Spatial Filtering     214
X[superscript (3)] Vector Soliton     215
Quantum Correlations Between Field Quadratures at Different Points     216
X[superscript (3)] Scalar Spatial Soliton     216
Vector Solitons     216
X[superscript (2)] Spatial Solitons     217
Conclusion     218
References     218
Quantum Fluctuations in Cavity Solitons   Gian-Luca Oppo   John Jeffers     221
Introduction     221
Cavity Solitons in Degenerate Optical Parametric Oscillators     222
Spatial Equations and Domain Walls with Oscillatory Tails     223
Cavity Solitons Formed by Locked Domain Walls     223
Quantum Fluctuations in DOPO     226
Wigner Representation     226
Q-Representation     227
Arrays of CS Induced by Quantum Fluctuations     227
Quantum Features in the Near and the Far Field of CS     231
Quantum Correlations of CS in the Near Field     231
Quantum Correlations of CS in the Far Field     233
Conclusions and Acknowledgments     236
References     236
Quantum Holographic Teleportation and Dense Coding of Optical Images   Ivan V. Sokolov      239
Introduction     239
Continuous-Variable Squeezing and Entanglement for Spatially Multimode Light Fields     240
Spatial Scales of Quantum Correlations in Squeezed Light     240
Spatially Multimode Entanglement     243
Quantum Holographic Teleportation of Optical Images     244
Basics of Quantum Teleportation     245
Optical Scheme for Quantum Teleportation of Images     246
Quantum Statistics of the Teleported Field     247
Global and Reduced Fidelity of Holographic Teleportation     254
Quantum Holographic Teleportation and Holography     259
Quantum Dense Coding of Optical Images     260
Basics of Quantum Dense Coding     260
Optical Scheme for Quantum Dense Coding of Images     261
Shannon Mutual Information for Images     264
Channel Capacity     266
Conclusions and Outlook     270
Properties of Spatially Multimode Squeezing     271
Homodyne Detection with Spatial Resolution     273
References     275
Orbital Angular Momentum of Light   Stephen M. Barnett   Roberta Zambrini     277
Introduction     277
Angular Momentum in Electromagnetism      278
Spin and Orbital Angular Momentum     280
Angular Momentum in Paraxial Optics     281
Mechanical Effects     283
Beams Carrying Orbital Angular Momentum     284
Phase Singularities and Spatial Properties     284
Laguerre-Gaussian and Bessel Beams     284
Generation and Conversion     286
Other Field Spatial Profiles     289
Fractional Orbital Angular Momentum     290
Quantum Optical Angular Momentum     290
States of Spin and Orbital Angular Momentum     290
Measuring Orbital Angular Momentum     291
Angle and Angular Momentum     292
Uncertainty Relation for Angle and Angular Momentum     292
Intelligent and Minimum Uncertainty Product States     294
Communications     297
Rotation Measurements     299
Orbital Angular Momentum in Quantum Nonlinear Optics     300
Phase Matching     301
Second-Harmonic Generation of Laguerre-Gaussian Beams     302
Down-Conversion and Entanglement     304
High-Order Nonlinearity     306
Conclusion     307
References     308
Index     313