Introductory Quantum Optics,9780521820356

Introductory Quantum Optics

by
ISBN13: 9780521820356
ISBN10: 0521820359
Format: Hardcover
Pub. Date: 2004-11-22
Publisher(s): Cambridge University Press
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Summary

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 xii
1 Introduction
1(9)
1.1 Scope and aims of this book
1(1)
1.2 History
2(5)
1.3 The contents of this book
7(1)
References
8(1)
Suggestions for further reading
8(2)
2 Field quantization
10(33)
2.1 Quantization of a single-mode field
10(5)
2.2 Quantum fluctuations of a single-mode field
15(2)
2.3 Quadrature operators for a single-mode field
17(1)
2.4 Multimode fields
18(7)
2.5 Thermal fields
25(4)
2.6 Vacuum fluctuations and the zero-point energy
29(4)
2.7 The quantum phase
33(7)
Problems
40(1)
References
41(1)
Bibliography
42(1)
3 Coherent states
43(31)
3.1 Eigenstates of the annihilation operator and minimum uncertainty states
43(5)
3.2 Displaced vacuum states
48(2)
3.3 Wave packets and time evolution
50(2)
3.4 Generation of coherent states
52(1)
3.5 More on the properties of coherent states
53(3)
3.6 Phase-space pictures of coherent states
56(3)
3.7 Density operators and phase-space probability distributions
59(6)
3.8 Characteristic functions
65(6)
Problems
71(1)
References
72(1)
Bibliography
73(1)
4 Emission and absorption of radiation by atoms
74(41)
4.1 Atom-field interactions
74(2)
4.2 Interaction of an atom with a classical field
76(6)
4.3 Interaction of an atom with a quantized field
82(5)
4.4 The Rabi model
87(3)
4.5 Fully quantum-mechanical model; the Jaynes-Cummings model
90(9)
4.6 The dressed states
99(3)
4.7 Density-operator approach: application to thermal states
102(3)
4.8 The Jaynes-Cummings model with large detuning: a dispersive interaction
105(2)
4.9 Extensions of the Jaynes--Cummings model
107(1)
4.10 Schmidt decomposition and von Neumann entropy for the Jaynes-Cummings model
108(2)
Problems
110(3)
References
113(1)
Bibliography
114(1)
5 Quantum coherence functions
115(20)
5.1 Classical coherence functions
115(5)
5.2 Quantum coherence functions
120(4)
5.3 Young's interference
124(3)
5.4 Higher-order coherence functions
127(6)
Problems
133(1)
References
133(1)
Bibliography
134(1)
6 Beam splitters and interferometers
135(15)
6.1 Experiments with single photons
135(2)
6.2 Quantum mechanics of beam splatters
137(6)
6.3 Interferometry with a single photon
143(1)
6.4 Interaction-free measurement
144(2)
6.5 Interferometry with coherent states of light
146(1)
Problems
147(2)
References
149(1)
Bibliography
149(1)
7 Nonclassical light
150(45)
7.1 Quadrature squeezing
150(15)
7.2 Generation of quadrature squeezed light
165(2)
7.3 Detection of quadrature squeezed light
167(2)
7.4 Amplitude (or number) squeezed states
169(2)
7.5 Photon antibunching
171(1)
7.6 Schrödinger cat states
171(11)
7.7 Two-mode squeezed vacuum states
182(6)
7.8 Higher-order squeezing
188(1)
7.9 Broadband squeezed light
189(1)
Problems
190(2)
References
192(2)
Bibliography
194(1)
8 Dissipative interactions and decoherence
195(18)
8.1 Introduction
195(1)
8.2 Single realizations or ensembles?
196(4)
8.3 Individual realizations
200(4)
8.4 Shelving and telegraph dynamics in three-level atoms
204(3)
8.5 Decoherence
207(1)
8.6 Generation of coherent states from decoherence: nonlinear optical balance
208(2)
8.7 Conclusions
210(1)
Problems
211(1)
References
211(1)
Bibliography
212(1)
9 Optical test of quantum mechanics
213(25)
9.1 Photon sources: spontaneous parametric down-conversion
214(3)
9.2 The Hong-Ou-Mandel interferometer
217(2)
9.3 The quantum eraser
219(3)
9.4 Induced coherence
222(2)
9.5 Superluminal tunneling of photons
224(2)
9.6 Optical test of local realistic theories and Bell's theorem
226(6)
9.7 Franson's experiment
232(1)
9.8 Applications of down-converted light to metrology without absolute standards
233(2)
Problems
235(1)
References
236(1)
Bibliography
237(1)
10 Experiments in cavity QED and with trapped ions 238(25)
10.1 Rydberg atoms
238(3)
10.2 Rydberg atom interacting with a cavity field
241(5)
10.3 Experimental realization of the Jaynes-Cummings model
246(3)
10.4 Creating entangled atoms in CQED
249(1)
10.5 Formation of Schrödinger cat states with dispersive atom-field interactions and decoherence from the quantum to the classical
250(4)
10.6 Quantum nondemolition measurement of photon number
254(1)
10.7 Realization of the Jaynes-Cummings interaction in the motion of a trapped ion
255(3)
10.8 Concluding remarks
258(1)
Problems
259(1)
References
260(1)
Bibliography
261(2)
11 Applications of entanglement: Heisenberg-limited interferometry and quantum information processing 263(31)
11.1 The entanglement advantage
264(1)
11.2 Entanglement and interferometric measurements
265(3)
11.3 Quantum teleportation
268(2)
11.4 Cryptography
270(1)
11.5 Private key crypto-systems
271(2)
11.6 Public key crypto-systems
273(1)
11.7 The quantum random number generator
274(1)
11.8 Quantum cryptography
275(6)
11.9 Future prospects for quantum communication
281(1)
11.10 Gates for quantum computation
281(5)
11.11 An optical realization of some quantum gates
286(3)
11.12 Decoherence and quantum error correction
289(1)
Problems
290(1)
References
291(2)
Bibliography
293(1)
Appendix A The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy 294(10)
A.1 The density operator
294(3)
A.2 Two-state system and the Bloch sphere
297(1)
A.3 Entangled states
298(1)
A.4 Schmidt decomposition
299(2)
A.5 von Neumann entropy
301(1)
A.6 Dynamics of the density operator
302(1)
References
303(1)
Bibliography
303(1)
Appendix B Quantum measurement theory in a (very small) nutshell 304(4)
Bibliography
307(1)
Appendix C Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions 308(4)
References
311(1)
Appendix D Nonlinear optics and spontaneous parametric down-conversion 312(2)
References
313(1)
Index 314

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