Quantum imaging

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. Contents......Page 7 1.1 Introduction......Page 15 1.2.1 Prototype Model I......Page 16 1.2.2 Prototype Model II......Page 17 1.3 Intrinsic Relation Between Squeezing and Entanglement......Page 19 1.4.1 Spatially Multimode Versus Single-Mode Squeezing: Optical Parametric Down-Conversion of Type-I......Page 21 1.4.2 Near-Field/Far-Field Duality in Type-I OPAs......Page 22 1.4.3 Detection of Weak Amplitude or Phase Objects Beyond the Standard Quantum Limit......Page 25 1.4.4 Image Amplification by Parametric Down-Conversion (Type-I)......Page 26 References......Page 28 2.2.1 Propagation Equations for the Signal–Idler Fields and Input-Output Relations......Page 30 2.2.2 Near- and Far-Field Correlations in the Stationary and Plane-Wave Pump Approximation......Page 35 2.2.4 Far-Field Correlations......Page 38 2.2.5 Near-Field Correlations......Page 39 2.3 Detection of Sub-Shot-Noise Spatial Correlations in High-Gain Parametric Down-Conversion......Page 41 2.3.1 Detection of the Spatial Features of the Far-Field PDC Radiation by Means of the CCD......Page 42 2.3.2 Experimental Set-Up for Spatial-Correlations Measurements......Page 43 2.3.3 Detection of Quantum Spatial Correlations: Spatial Analogue of Photon Antibunching in Time......Page 46 2.4 Multiphoton, Multimode Polarization Entanglement in Parametric Down-Conversion......Page 51 References......Page 56 3.2.1 Introduction......Page 59 3.2.2 Cavity Round-Trip Transform......Page 60 3.2.3 Image Transmission Through an Optical Cavity......Page 62 3.3.1 Classical Behavior......Page 64 3.3.2 Quantum Properties......Page 66 3.4 Experimental Results......Page 69 3.4.1 Classical Effects: Observation of Optical Patterns......Page 70 3.4.2 Observation of Quantum Correlations in Images......Page 71 References......Page 75 4.1 Introduction......Page 78 4.2 Quantum Noise in an Arraylike Detection......Page 79 4.3 Implementing a Sub-Shot-Noise Array Detection......Page 81 4.4 The Quantum Laser Pointer......Page 82 4.5 Optical Read-Out......Page 84 4.6 Measuring a Signal in an Optimal Way......Page 87 4.7 Conclusion......Page 88 References......Page 89 5.1 Introduction......Page 90 5.2 General Theory of Ghost Imaging with Entangled Beams......Page 92 5.2.1 Specific Imaging Schemes......Page 94 5.3 Wave-Particle Aspect......Page 96 5.4 Spatial Average in Ghost Diffraction: Increase of Spatial Bandwidth and of Speed in Retrieval......Page 98 5.5 Ghost Imaging with Homodyne Detection......Page 99 5.6 Debate: Is Quantum Entanglement Really Necessary for Ghost Imaging?......Page 101 5.7 Ghost Imaging by Split Thermallike Beams: Theory [15–17]......Page 103 5.7.1 Analogy Between Thermal and Entangled Beams in Ghost Imaging [15–17]......Page 104 5.7.3 Relations with the Classic Hanburry–Brown and Twiss Correlation Technique [37]......Page 106 5.7.4 Correlation Aspects......Page 107 5.7.5 Visibility Aspects......Page 109 5.7.7 Rule-of-Thumb Comparison Between Entangled and "Thermal" Ghost Imaging......Page 111 5.8 Ghost Imaging with Split Thermal Beams: Experiment......Page 112 5.8.1 High-Resolution Ghost Imaging [23]......Page 113 5.8.2 The Ghost Diffraction Experiment: Complementarity Between Coherence and Correlation [24]......Page 118 References......Page 121 6.1 Super-Resolution in Classical Optics......Page 123 6.2.1 Quantum Theory of Optical Imaging......Page 125 6.2.2 Quantum Theory of Optical Fourier Microscopy......Page 129 6.3.1 Reconstruction of Classical Noise-Free Objects......Page 131 6.3.2 Reconstruction of Objects with Quantum Fluctuations......Page 136 6.3.3 Point-Spread Function for Super-Resolving Reconstruction of Objects......Page 138 6.4 Squeezed-Light Source for Microscopy with Super-Resolution......Page 142 References......Page 148 7.1 Introduction......Page 150 7.2 Traveling-Wave Scheme for Amplification of Images......Page 151 7.3 Optimum Phase Matching for Parametric Amplification......Page 154 7.4 Quantum Fluctuations in the Amplified Image and Conditions for Noiseless Amplification......Page 158 7.5 Experimental Demonstration of Temporally Noiseless Image Amplification......Page 164 7.6 Experiment on Spatially Noiseless Amplification of Images......Page 167 References......Page 173 8.1 Introduction......Page 175 8.2 Image Processing in Second-Harmonic Generation at a Classical Level......Page 176 8.2.1 Frequency Up-Conversion of an Image......Page 179 8.2.2 Contrast Enhancement and Contour Recognition......Page 180 8.2.3 Noise Filtering Properties......Page 182 8.3 Quantum Image Processing in Type-I Second-Harmonic Generation......Page 183 8.3.1 Field-Operator Dynamics......Page 184 8.3.2 Quantum Image Processing......Page 189 8.4 Quantum Image Processing in Type-II Second-Harmonic Generation......Page 196 8.4.1 Propagation Equations......Page 197 8.4.2 Linearly y-Polarized Pump: Frequency Addition Regime......Page 200 8.4.3 45o-Linearly Polarized Pump: Noiseless Up-Conversion and Amplification......Page 201 References......Page 207 9.1 Introduction......Page 209 9.2.1 Propagation Equations for the Fluctuations......Page 210 9.2.2 Green's Function Approach......Page 211 9.2.3 Correlations Between the Photocurrents......Page 212 9.3.1 χ[sup((3))] Scalar Spatial Soliton......Page 213 9.3.3 χ[sup((2))] Spatial Soliton......Page 214 9.4.2 χ[sup((3))] Vector Soliton: Total Beam Squeezing and Correlation Between Polarizations......Page 216 9.4.3 χ[sup((2))] Spatial Solitons......Page 218 9.5.1 χ[sup((3))] Scalar Spatial Soliton......Page 219 9.5.2 Intensity Squeezing by Spatial Filtering......Page 222 9.5.3 χ[sup((3))] Vector Soliton......Page 223 9.6.2 Vector Solitons......Page 224 9.6.3 χ[sup((2))]Spatial Solitons......Page 225 References......Page 226 10.1 Introduction......Page 228 10.2 Cavity Solitons in Degenerate Optical Parametric Oscillators......Page 229 10.2.2 Cavity Solitons Formed by Locked Domain Walls......Page 230 10.3.1 Wigner Representation......Page 233 10.4 Arrays of CS Induced by Quantum Fluctuations......Page 234 10.5.1 Quantum Correlations of CS in the Near Field......Page 238 10.5.2 Quantum Correlations of CS in the Far Field......Page 240 References......Page 243 11.1 Introduction......Page 245 11.2.1 Spatial Scales of Quantum Correlations in Squeezed Light......Page 246 11.2.2 Spatially Multimode Entanglement......Page 249 11.3 Quantum Holographic Teleportation of Optical Images......Page 250 11.3.1 Basics of Quantum Teleportation......Page 251 11.3.2 Optical Scheme for Quantum Teleportation of Images......Page 252 11.3.3 Quantum Statistics of the Teleported Field......Page 253 11.3.4 Global and Reduced Fidelity of Holographic Teleportation......Page 260 11.3.5 Quantum Holographic Teleportation and Holography......Page 265 11.4.1 Basics of Quantum Dense Coding......Page 266 11.4.2 Optical Scheme for Quantum Dense Coding of Images......Page 267 11.4.3 Shannon Mutual Information for Images......Page 270 11.4.4 Channel Capacity......Page 272 11.5 Conclusions and Outlook......Page 276 A. Properties of Spatially Multimode Squeezing......Page 277 B. Homodyne Detection with Spatial Resolution......Page 279 References......Page 281 12.1 Introduction......Page 283 12.2 Angular Momentum in Electromagnetism......Page 284 12.2.1 Spin and Orbital Angular Momentum......Page 286 12.2.2 Angular Momentum in Paraxial Optics......Page 287 12.2.3 Mechanical Effects......Page 289 12.3.2 Laguerre–Gaussian and Bessel Beams......Page 290 12.3.3 Generation and Conversion......Page 292 12.3.4 Other Field Spatial Profiles......Page 295 12.4.1 States of Spin and Orbital Angular Momentum......Page 296 12.4.2 Measuring Orbital Angular Momentum......Page 297 12.5.1 Uncertainty Relation for Angle and Angular Momentum......Page 298 12.5.2 Intelligent and Minimum Uncertainty Product States......Page 300 12.5.3 Communications......Page 303 12.5.4 Rotation Measurements......Page 305 12.6 Orbital Angular Momentum in Quantum Nonlinear Optics......Page 306 12.6.1 Phase Matching......Page 307 12.6.2 Second-Harmonic Generation of Laguerre–Gaussian Beams......Page 308 12.6.3 Down-Conversion and Entanglement......Page 310 12.6.4 High-Order Nonlinearity......Page 312 12.7 Conclusion......Page 313 References......Page 314 G......Page 318 P......Page 319 S......Page 320 W......Page 321 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. This book contains the most important theoretical and experimental results achieved by the researchers of the Quantum Imaging network, a research programme of the European Community. Quantum Imaging is a branch of quantum optics that investigates the ultimate performance limits of optical imaging allowed by the laws of quantum mechanics. This book gives an overview of the progress in the domain of quantum imaging. It reflects research carried out by leading specialists in the area within the Quantum Imaging network