Quantum Imaging

By: Mikhail I. Kolobov (Editor)

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Hardcover | 25 October 2006

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332 Pages

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24.13 x 16.51 x 2.54

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This book gives an overview of the latest progress in the domain of quantum imaging. It reflects three and a half years of research carried out by leading specialists in the area within the Quantum Imaging network, a research programme of the European Community.

Quantum Imaging is a newly born branch of quantum optics that investigates the ultimate performance limits of optical imaging allowed by the laws of quantum mechanics. Using the methods and techniques from quantum optics, quantum imaging addresses the questions of image formation, processing and detection with sensitivity and resolution exceeding the limits of classical imaging.

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Non-Fiction Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Engineering & Technology Other Technologies & Applied Sciences Applied Optics Optical Physics

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

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