Quantum Optics

Contents......Page 10
Introduction......Page 16
1 The quantum nature of light......Page 18
1.1 The early experiments......Page 20
1.2 Photons......Page 28
1.3 Are photons necessary?......Page 35
1.4 Indivisibility of photons......Page 39
1.5 Spontaneous down-conversion light source......Page 43
1.7 The quantum theory of light......Page 44
1.8 Exercises......Page 45
2.1 Quantization of cavity modes......Page 47
2.2 Normal ordering and zero-point energy......Page 62
2.3 States in quantum theory......Page 63
2.4 Mixed states of the electromagnetic field......Page 70
2.5 Vacuum fluctuations......Page 75
2.6 The Casimir effect......Page 77
2.7 Exercises......Page 80
3.1 Field quantization in the vacuum......Page 84
3.2 The Heisenberg picture......Page 98
3.3 Field quantization in passive linear media......Page 102
3.4 Electromagnetic angular momentum*......Page 115
3.5 Wave packet quantization*......Page 118
3.6 Photon localizability*......Page 121
3.7 Exercises......Page 124
4.1 Semiclassical electrodynamics......Page 126
4.2 Quantum electrodynamics......Page 128
4.3 Quantum Maxwell’s equations......Page 132
4.4 Parity and time reversal*......Page 133
4.5 Stationary density operators......Page 136
4.6 Positive- and negative-frequency parts for interacting fields......Page 137
4.7 Multi-time correlation functions......Page 138
4.8 The interaction picture......Page 139
4.9 Interaction of light with atoms......Page 145
4.10 Exercises......Page 160
5.1 Quasiclassical states for radiation oscillators......Page 163
5.2 Sources of coherent states......Page 168
5.3 Experimental evidence for Poissonian statistics......Page 172
5.4 Properties of coherent states......Page 176
5.5 Multimode coherent states......Page 182
5.6 Phase space description of quantum optics......Page 187
5.7 Gaussian states*......Page 202
5.8 Exercises......Page 205
6.1 Einstein–Podolsky–Rosen states......Page 208
6.2 Schrödinger’s concept of entangled states......Page 209
6.3 Extensions of the notion of entanglement......Page 210
6.4 Entanglement for distinguishable particles......Page 215
6.5 Entanglement for identical particles......Page 220
6.6 Entanglement for photons......Page 225
6.7 Exercises......Page 231
7 Paraxial quantum optics......Page 233
7.2 Paraxial states......Page 234
7.3 The slowly-varying envelope operator......Page 238
7.4 Gaussian beams and pulses......Page 241
7.5 The paraxial expansion*......Page 243
7.6 Paraxial wave packets*......Page 244
7.7 Angular momentum*......Page 245
7.8 Approximate photon localizability*......Page 247
7.9 Exercises......Page 249
8.1 Classical scattering......Page 252
8.2 Quantum scattering......Page 257
8.3 Paraxial optical elements......Page 260
8.4 The beam splitter......Page 262
8.5 Y-junctions......Page 269
8.6 Isolators and circulators......Page 270
8.7 Stops......Page 275
8.8 Exercises......Page 277
9.1 Primary photon detection......Page 280
9.2 Postdetection signal processing......Page 295
9.3 Heterodyne and homodyne detection......Page 305
9.4 Exercises......Page 320
10.1 Single-photon interference......Page 322
10.2 Two-photon interference......Page 330
10.3 Single-photon interference revisited*......Page 348
10.4 Tunneling time measurements*......Page 352
10.5 The meaning of causality in quantum optics*......Page 358
10.6 Interaction-free measurements*......Page 360
10.7 Exercises......Page 363
11.1 Resonant wave approximation......Page 365
11.2 Spontaneous emission II......Page 372
11.3 The semiclassical limit......Page 384
11.4 Exercises......Page 394
12.1 The Jaynes–Cummings model......Page 396
12.2 Collapses and revivals......Page 399
12.3 The micromaser......Page 402
12.4 Exercises......Page 405
13.1 The atomic polarization......Page 406
13.2 Weakly nonlinear media......Page 408
13.3 Three-photon interactions......Page 414
13.4 Four-photon interactions......Page 427
13.5 Exercises......Page 433
14.1 The world as sample and environment......Page 435
14.2 Photons in a lossy cavity......Page 443
14.3 The input–output method......Page 450
14.4 Noise and dissipation for atoms......Page 457
14.5 Incoherent pumping......Page 462
14.6 The fluctuation dissipation theorem*......Page 465
14.7 Quantum regression*......Page 469
14.8 Photon bunching*......Page 471
14.9 Resonance fluorescence*......Page 472
14.10 Exercises......Page 481
15.1 Squeezed states......Page 485
15.2 Theory of squeezed-light generation*......Page 500
15.3 Experimental squeezed-light generation......Page 507
15.4 Number states......Page 510
15.5 Exercises......Page 512
16.1 General properties of linear amplifiers......Page 514
16.2 Regenerative amplifiers......Page 517
16.3 Traveling-wave amplifiers......Page 525
16.4 General description of linear amplifiers......Page 531
16.5 Noise limits for linear amplifiers......Page 538
16.6 Exercises......Page 542
17.1 Classical tomography......Page 544
17.2 Optical homodyne tomography......Page 547
17.3 Experiments in optical homodyne tomography......Page 548
17.4 Exercises......Page 552
18.2 The environment picture......Page 553
18.3 Averaging over the environment......Page 554
18.4 Examples of the master equation......Page 557
18.5 Phase space methods......Page 561
18.6 The Lindblad form of the master equation*......Page 571
18.7 Quantum jumps......Page 572
18.8 Exercises......Page 591
19 Bell's theorem and its optical tests......Page 593
19.1 The Einstein–Podolsky–Rosen paradox......Page 594
19.2 The nature of randomness in the quantum world......Page 596
19.3 Local realism......Page 598
19.4 Bell's theorem......Page 604
19.5 Quantum theory versus local realism......Page 606
19.6 Comparisons with experiments......Page 611
19.7 Exercises......Page 615
20.1 Telecommunications......Page 616
20.2 Quantum cloning......Page 621
20.3 Quantum cryptography......Page 631
20.4 Entanglement as a quantum resource......Page 634
20.5 Quantum computing......Page 645
20.6 Exercises......Page 654
A.2 General vector spaces......Page 660
A.3 Hilbert spaces......Page 661
A.4 Fourier transforms......Page 666
A.5 Laplace transforms......Page 669
A.6 Functional analysis......Page 670
A.7 Improper functions......Page 671
A.8 Probability and random variables......Page 674
B.1 Maxwell's equations......Page 676
B.2 Electrodynamics in the frequency domain......Page 677
B.3 Wave equations......Page 678
B.4 Planar cavity......Page 684
B.5 Macroscopic Maxwell equations......Page 685
C.1 Dirac's bra and ket notation......Page 695
C.2 Physical interpretation......Page 698
C.3 Useful results for operators......Page 700
C.4 Canonical commutation relations......Page 705
C.5 Angular momentum in quantum mechanics......Page 707
C.6 Minimal coupling......Page 708
References......Page 710
C......Page 723
D......Page 724
H......Page 725
L......Page 726
P......Page 727
S......Page 729
T......Page 730
Z......Page 731