Essential Quantum Optics: From Quantum Measurements to Black Holes

by Ulf Leonhardt

• ISBN13: 9780521869782
• ISBN10: 0521869781
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-03-29
• Publisher: Cambridge University Press

Summary

Covering some of the most exciting trends in quantum optics - quantum entanglement, teleportation, and levitation - this textbook is ideal for advanced undergraduate and graduate students. The book journeys through the vast field of quantum optics following a single theme: light in media. A wide range of subjects are covered, from the force of the quantum vacuum to astrophysics, from quantum measurements to black holes. Ideas are explained in detail and formulated so that students with little prior knowledge of the subject can follow them. Each chapter ends with several short questions followed by a more detailed homework problem, designed to test the reader and show how the ideas discussed can be applied. Solutions to homework problems are available at www.cambridge.org/9780521869782.

Author Biography

Ulf Leonhardt is Professor of Theoretical Physics at the University of St Andrews. His research interests include quantum electrodynamics in media and state reconstruction in quantum mechanics. He is one of the inventors of invisibility devices and artificial black holes.

Table of Contents

Acknowledgements	p. xi
Introduction	p. 1
A note to the reader	p. 1
Quantum theory	p. 3
Axioms	p. 3
Quantum statistics	p. 7
Schrödinger and Heisenberg pictures	p. 10
On the questions and homework problems	p. 12
Further reading	p. 13
Quantum field theory of light	p. 14
Light in media	p. 14
Maxwell's equations	p. 14
Quantum commutator	p. 16
Light modes	p. 19
Modes and their scalar product	p. 20
Bose commutation relations	p. 22
Interference	p. 23
Monochromatic modes	p. 25
Zero-point energy and Casimir force	p. 27
An attractive cavity	p. 27
Reflections	p. 30
Questions	p. 32
Homework problem	p. 33
Further reading	p. 35
Simple quantum states of light	p. 37
The electromagnetic oscillator	p. 37
Single-mode states	p. 40
Quadrature states	p. 40
Fock states	p. 41
Thermal states	p. 45
Coherent states	p. 48
Uncertainty and squeezing	p. 53
Questions	p. 60
Homework problem	p. 61
Further reading	p. 62
Quasiprobability distributions	p. 63
Wigner representation	p. 63
Wigner's formula	p. 64
Basic properties	p. 68
Examples	p. 73
Other quasiprobability distributions	p. 79
Q function	p. 80
P function	p. 81
s-parameterized quasiprobability distributions	p. 82
Examples	p. 85
Questions	p. 89
Homework problem	p. 90
Further reading	p. 91
Simple optical instruments	p. 92
Beam splitter	p. 92
Heisenberg picture	p. 92
Schrödinger picture	p. 96
Fock representation and wave-particle dualism	p. 103
Detection	p. 106
Photodetector	p. 107
Balanced homodyne detection	p. 110
Quantum tomography	p. 113
Simultaneous measurement of conjugate variables	p. 119
Questions	p. 131
Homework problem	p. 133
Further reading	p. 134
Irrevesible processes	p. 135
Lindblad's theorem	p. 135
Irreversibility	p. 135
Reversible dynamics	p. 137
Irreversible dynamics	p. 137
Loss and gain	p. 140
Absorption and amplification	p. 140
Absorber	p. 144
Amplifier	p. 147
Eavesdropper	p. 150
Continuous quantum measurements	p. 151
Questions	p. 155
Homework problem	p. 156
Further reading	p. 158
Entanglement	p. 159
Parametric amplifier	p. 159
Heisenberg picture	p. 159
Schrödinger picture	p. 160
Einstein-Podolski-Rosen state	p. 167
Quantum teleportation	p. 171
Polarization correlations	p. 175
Singlet state	p. 175
Polarization	p. 178
Bell's theorem	p. 182
Questions	p. 185
Homework problem	p. 187
Further reading	p. 188
Horizons	p. 189
Minkowski space	p. 189
Locality and relativity	p. 191
Space-time geometry	p. 195
Light	p. 197
Accelerated observers	p. 199
Rindler coordinates	p. 200
Accelerated modes	p. 203
Unruh effect	p. 205
Moving media	p. 209
Motivation	p. 211
Trans-Planckian problem	p. 214
Light in moving media	p. 217
Geometry of light	p. 219
Hawking radiation	p. 221
Questions	p. 227
Homework problem	p. 229
Further reading	p. 229
Stress of the quantum vacuum	p. 231
State reconstruction in quantum mechanics	p. 250
References	p. 262
Index	p. 274
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