Quantum Squeezing

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Springer Science & Business Media, 22 ene. 2004 - 370 páginas
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The concept of squeezing is intimately related to the idea of vacuum fluctu ations, once thought to place an absolute limit to the accuracy of measure ment. However, vacuum fluctuations are not unchangeable. By recognizing that these quantum fluctuations always occur in two complementary observ ables, physicists have been able to make an intriguing trade-off. Reduced fluctuations in one variable can be realized - at the expense of increased fluctuations in another, according to Heisenberg. This Heisenberg 'horse-trade' - originally predicted by theorists - was first accomplished experimentally by R. Slusher in 1985. Since then, the var ious techniques and applications of quantum squeezing have metamorphosed into a central tool in the wider field of quantum information. This book is a summary of the main ideas, methods and applications of quantum squeezing, written by those responsible for some of the chief developments in the field. The book is divided into three parts, to recognize that there are three areas in this research. These are the fundamental physics of quantum fluc tuations, the techniques of generating squeezed radiation, and the potential applications. Part I of the book, giving the fundamentals, is arranged as follows. • Chapter 1 introduces the basic ideas about what squeezing of quantum fluctuations is from the quantized free-field perspective. This chapter es tablishes the definitions and notations used throughout. • Chapter 2 explains how to quantize radiation in a dielectric, which is the basic technique that is used to make squeezed radiation.
 

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Squeezed States Basic Principles
3
111 Quantization of the Electromagnetic Field
5
112 Uncertainty Relations and Squeezing of Quantum Fluctuations
6
113 WeylHeisenberg Algebra and Quadrature Squeezing
7
12 Quantum States of Light Fields
8
122 Fock States
12
123 Coherent States
13
124 Squeezed States
15
623 InLoop and OutofLoop Spectra
181
624 Commutation Relations
184
625 Semiclassical Theory
185
626 QND Measurements of InLoop Beams
187
627 A Squeezed Input
188
63 Quantum Langevin Equations
189
64 Feedback Based on Nonlinear Measurements
191
642 QNDBased Feedback
193

125 TwoMode Squeezed Vacuum
19
Quantum Interference in Phase Space
21
14 Superpositions of Coherent States
26
15 Onedimensional Continuous Superpositions of Coherent States
29
16 Conclusion
30
Nonlinear Dielectrics
33
21 Macroscopic Approach
34
211 Vector Potential Quantization
35
212 Dual Potential Quantization
36
22 Mode Expansion
38
23 Dispersion
39
24 Microscopic Approach
44
25 Conclusion
50
InputOutput Theory
53
31 Free Fields
55
32 Harmonic Oscillator Coupled to a Transmission Line
57
33 Field Theoretic Approach to InputOutput Theory
61
34 Approximations
63
35 Alternative Approach to InputOutput Theory
67
36 Scattering Matrices Within the Markov Approximation
72
37 Reflection Parametric Amplifier
73
38 Homodyne Detection
74
39 Multiple Ports
80
310 Phase Shifters
82
311 Beam Splitters
83
312 Resonators
85
313 Lossy Transmission Lines
88
314 Attenuators
94
References
95
Generation of Quantum Squeezing
97
Squeezing with Nonlinear Optics
99
41 Transient Squeezing
100
42 Driven Parametric Oscillator
102
43 Observable Moments and Spectra
105
44 Heisenberg and Classical Equations
107
45 FokkerPlanck and Stochastic Equations
112
46 BelowThreshold Perturbation Theory
115
461 Matched Power Equations
116
462 External Squeezing Correlations
118
463 Optimal Squeezing
119
464 Experiments
122
47 Waveguides and Fibers
123
472 Nonlinear Schrodinger Equation
125
473 Parametric Operator Equations
127
474 Squeezed Propagation
128
475 Quadrature Variances
130
476 Photon Number Correlations
131
481 RamanSchrodinger Model
132
482 Initial Conditions and Quantum Evolution
133
484 Experiments
135
49 Conclusion
136
References
137
Squeezing from Lasers
141
51 The Laser Model
142
511 The Hamiltonian
144
512 The Quantum Langevin Equation
145
513 Laser Rate Equations
147
514 Linearized Fluctuation Equations
149
515 Noise Spectra
151
516 Phenomenological SemiClassical Equations
152
52 Squeezing from the Rate Equation Model
153
522 Regularized Pumping
154
524 Inversion Filtering
157
525 Squeezing Efficiency
158
526 Squeezing Under NonIdeal Conditions
160
53 Squeezing from Coherent Effects
161
531 Extending the Laser Model
163
532 Squeezing from Coherent Pumping
165
54 Conclusion
166
55 Expectation Values
167
56 SemiClassical Solutions
168
References
169
Squeezing and Feedback
171
61 Continuum Fields
173
612 Photodetection
176
62 InLoop Squeezing
178
622 Stability
180
643 Parametric Down Conversion
195
644 Second Harmonic Generation
196
65 Quantum Trajectories
197
652 Photon Counting
199
653 Homodyne Detection Theory
201
654 HomodyneMediated Feedback
202
66 Intracavity Squeezing
203
662 HomodyneMediated Feedback
205
663 QNDMediated Feedback
208
664 Mimicking a Squeezed Bath
210
665 The Micromaser
211
68 InLoop Squeezing Revisited
212
682 An InLoop Atom
215
683 Comparison with Free Squeezing
217
684 Other Uses of Squashed Light
219
69 Conclusion
220
References
222
Applications of Quantum Squeezing
225
Communication and Measurement with Squeezed States
227
71 Classical Communication and Measurement
229
712 Signal Noise and Dimensionality
232
713 Communication versus Measurement
236
72 Quantum Communication
237
722 Mutual Information
239
723 The Entropy Bound
242
724 Effect of Loss
243
725 Quantum Amplifiers and Duplicators
244
73 Ultimate Limit on Measurement Accuracy
248
732 Classical RateDistortion Limit
251
733 Ultimate Quantum Measurement System Limit
253
74 Position Monitoring with Contractive States
255
References
258
Novel Spectroscopy with TwoLevel Atoms in Squeezed Fields
263
81 Theoretical Description of the Interaction of Squeezed Light with a TwoLevel Atom
266
82 The TwoLevel Atom in Free Space
268
822 The Dipole Decay Rates
269
823 Resonance Fluorescence
270
824 Anomalous Resonance Fluorescence
273
825 Pure Atomic States
277
826 Optimum Squeezing in the Output Field
280
827 Amplification of a Weak Probe Beam
282
828 Arbitrary Intensity Probe
285
829 Dressed State Population Trapping
286
83 TwoLevel Atoms in the Cavity Environment
290
831 The Mean Photon Number
291
832 The Bad Cavity Limit
292
833 The FabryPerot Microcavity
293
834 Bichromatic Excitation
295
84 Finite Bandwidth Sources
297
85 Systems of Na TwoLevel Atoms
300
852 Effect of Finite Separations
301
853 Two NonIdentical Atoms
304
References
305
Spectroscopy with ThreeLevel Atoms in a Squeezed Field
311
Master Equation
313
92 Equations of Motion for the Density Matrix Elements
320
93 Spontaneous Emission in a Squeezed Vacuum
322
94 Stationary Lineshape in a Squeezed Vacuum
329
95 Quantum Interference with Squeezed Light
330
96 Conclusion
333
EinsteinPodolskyRosen Correlations Entanglement and Quantum Cryptography
337
101 Generalization of the EPR Argument to Give Criteria for EPR Correlations
339
1011 Generalized EPR Argument
340
1012 1989 Inferred Heisenberg Uncertainty EPR Criterion
342
102 EPR Correlations from TwoMode Squeezed Light
344
103 Generalized EPR Criteria
346
104 Generalized EPR Correlations and Entanglement
349
1041 1989 EPR Criterion as a Signature of Entanglement
350
1042 A Signature of Entanglement Defined Through Observation of TwoMode Squeezing
351
1043 Generalized EPR Correlations Deduced Through Demonstrations of Entanglement
353
1044 Relationship to Stronger Entanglement Criteria Based on BellType Inequalities
356
1045 Entanglement is Implied Through Demonstrations of EPR Correlations
357
105 Application of EPR TwoMode Squeezed States to Quantum Cryptography
358
References
362
Bibliography
365
Index
367
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Sobre el autor (2004)

Peter D. Drummond is a Distinguished Professor in the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology. His current research focuses on ultra-cold atomic physics, quantum information and bio-informatics.

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