Introductory Quantum Optics (Paperback)

Description:

This elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter, is almost entirely concerned with the quantized electromagnetic field. The text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second- year graduate students.

Table of Contents:

 

Acknowledgements		page xii
1 Introduction		1
1.1 Scope and aims of this book		1
1.2 History		2
1.3 The contents of this book		7
	References	8
	Suggestions for further reading	8
2 Field quantization		10
2.1 Quantization of a single-mode field		10
2.2 Quantum fluctuations of a single-mode field		15
2.3 Quadrature operators for a single-mode field		17
2.4 Multimode fields		18
2.5 Thermal fields		25
2.6 Vacuum fluctuations and the zero-point energy		29
2.7 The quantum phase		33
	Problems	40
	References	41
	Bibliography	42
3 Coherent states		43
3.1 Eigenstates of the annihilation operator and minimum uncertainty states		43
3.2 Displaced vacuum states		48
3.3 Wave packets and time evolution		50
3.4 Generation of coherent states		52
3.5 More on the properties of coherent states		53
3.6 Phase-space pictures of coherent states		56
3.7 Density operators and phase-space probability distributions		59
3.8 Characteristic functions		65
	Problems	71
	References	72
	Bibliography	73
4 Emission and absorption of radiation by atoms		74
4.1 Atom–field interactions		74
4.2 Interaction of an atom with a classical field		76
4.3 Interaction of an atom with a quantized field		82
4.4 The Rabi model		87
4.5 Fully quantum-mechanical model; the Jaynes–Cummings model		90
4.6 The dressed states		99
4.7 Density-operator approach: application to thermal states		102
4.8 The Jaynes–Cummings model with large detuning: a dispersive interaction		105
4.9 Extensions of the Jaynes–Cummings model		107
4.10 Schmidt decomposition and von Neumann entropy for the Jaynes–Cummings model		108
	Problems	110
	References	113
	Bibliography	114
5 Quantum coherence functions		115
5.1 Classical coherence functions		115
5.2 Quantum coherence functions		120
5.3 Young’s interference		124
5.4 Higher-order coherence functions		127
	Problems	133
	References	133
	Bibliography	134
6 Beam splitters and interferometers		135
6.1 Experiments with single photons		135
6.2 Quantum mechanics of beam splitters		137
6.3 Interferometry with a single photon		143
6.4 Interaction-free measurement		144
6.5 Interferometry with coherent states of light		146
	Problems	147
	References	149
	Bibliography	149
7 Nonclassical light		150
7.1 Quadrature squeezing		150
7.2 Generation of quadrature squeezed light		165
7.3 Detection of quadrature squeezed light		167
7.4 Amplitude (or number) squeezed states		169
7.5 Photon antibunching		171
7.6 Schrödinger cat states		174
7.7 Two-mode squeezed vacuum states		182
7.8 Higher-order squeezing		188
7.9 Broadband squeezed light		189
	Problems	190
	References	192
	Bibliography	194
8 Dissipative interactions and decoherence		195
8.1 Introduction		195
8.2 Single realizations or ensembles?		196
8.3 Individual realizations		200
8.4 Shelving and telegraph dynamics in three-level atoms		204
8.5 Decoherence		207
8.6 Generation of coherent states from decoherence: nonlinear optical balance		208
8.7 Conclusions		210
	Problems	211
	References	211
	Bibliography	212
9 Optical test of quantum mechanics		213
9.1 Photon sources: spontaneous parametric down-conversion		214
9.2 The Hong–Ou–Mandel interferometer		217
9.3 The quantum eraser		219
9.4 Induced coherence		222
9.5 Superluminal tunneling of photons		224
9.6 Optical test of local realistic theories and Bell’s theorem		226
9.7 Franson’s experiment		232
9.8 Applications of down-converted light to metrology without absolute standards		233
	Problems	235
	References	236
	Bibliography	237
10 Experiments in cavity QED and with trapped ions		238
10.1 Rydberg atoms		238
10.2 Rydberg atom interacting with a cavity field		241
10.3 Experimental realization of the Jaynes–Cummings model		246
10.4 Creating entangled atoms in CQED		249
10.5 Formation of Schrödinger cat states with dispersive atom–field interactions and decoherence from the quantum to the classical		250
10.6 Quantum nondemolition measurement of photon number		254
10.7 Realization of the Jaynes–Cummings interaction in the motion of a trapped ion		255
10.8 Concluding remarks		258
	Problems	259
	References	260
	Bibliography	261
11 Applications of entanglement: Heisenberg-limited interferometry and quantum information processing		263
11.1 The entanglement advantage		264
11.2 Entanglement and interferometric measurements		265
11.3 Quantum teleportation		268
11.4 Cryptography		270
11.5 Private key crypto-systems		271
11.6 Public key crypto-systems		273
11.7 The quantum random number generator		274
11.8 Quantum cryptography		275
11.9 Future prospects for quantum communication		281
11.10 Gates for quantum computation		281
11.11 An optical realization of some quantum gates		286
11.12 Decoherence and quantum error correction		289
	Problems	290
	References	291
	Bibliography	293
	Appendix A The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy	294
A.1 The density operator		294
A.2 Two-state system and the Bloch sphere		297
A.3 Entangled states		298
A.4 Schmidt decomposition		299
A.5 von Neumann entropy		301
A.6 Dynamics of the density operator		302
	References	303
	Bibliography	303
	Appendix B Quantum measurement theory in a (very small) nutshell	304
	Bibliography	307
	Appendix C Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions	308
	References	311
	Appendix D Nonlinear optics and spontaneous parametric down-conversion	312
	References	313
Index		314