The Quantum Theory of Light Book

	Introduction: The photon	1
1	Planck's radiation law and the Einstein coefficients	3
1.1	Density of field modes in a cavity	4
1.2	Quantization of the field energy	7
1.3	Planck's law	10
1.4	Fluctuations in photon number	13
1.5	Einstein's A and B coefficients	16
1.6	Characteristics of the three Einstein transitions	19
1.7	Optical excitation of two-level atoms	23
1.8	Theory of optical attenuation	27
1.9	Population inversion: optical amplification	31
1.10	The laser	35
1.11	Radiation pressure	40
	References	44
2	Quantum mechanics of the atom-radiation interaction	46
2.1	Time-dependent quantum mechanics	46
2.2	Form of the interaction Hamiltonian	49
2.3	Expressions for the Einstein coefficients	52
2.4	The Dirac delta-function and Fermi's golden rule	57
2.5	Radiative broadening and linear susceptibility	60
2.6	Doppler broadening and composite lineshape	65
2.7	The optical Bloch equations	68
2.8	Power broadening	72
2.9	Collision broadening	76
2.10	Bloch equations and rate equations	79
	References	81
3	Classical theory of optical fluctuations and coherence	82
3.1	Models of chaotic light sources	83
3.2	The lossless optical beam-splitter	88
3.3	The Mach-Zehnder interferometer	91
3.4	Degree of first-order coherence	94
3.5	Interference fringes and frequency spectra	100
3.6	Intensity fluctuations of chaotic light	103
3.7	Degree of second-order coherence	107
3.8	The Brown-Twiss interferometer	114
3.9	Semiclassical theory of optical detection	117
	References	123
4	Quantization of the radiation field	125
4.1	Potential theory for the classical electromagnetic field	126
4.2	The free classical field	130
4.3	The quantum-mechanical harmonic oscillator	133
4.4	Quantization of the electromagnetic field	139
4.5	Canonical commutation relation	144
4.6	Pure states and statistical mixtures	148
4.7	Time development of quantum-optical systems	153
4.8	Interaction of the quantized field with atoms	155
4.9	Second quantization of the atomic Hamiltonian	162
4.10	Photon absorption and emission rates	168
4.11	The photon intensity operator	173
4.12	Quantum degrees of first and second-order coherence	176
	References	178
5	Single-mode quantum optics	180
5.1	Single-mode field operators	181
5.2	Number states	184
5.3	Coherent states	190
5.4	Chaotic light	199
5.5	The squeezed vacuum	201
5.6	Squeezed coherent states	206
5.7	Beam-splitter input-output relations	212
5.8	Single-photon input	216
5.9	Arbitrary single-arm input	221
5.10	Nonclassical light	227
	References	231
6	Multimode and continuous-mode quantum optics	233
6.1	Multimode states	234
6.2	Continuous-mode field operators	237
6.3	Number states	242
6.4	Coherent states	245
6.5	Chaotic light: photon bunching and antibunching	248
6.6	The Mach-Zehnder interferometer	251
6.7	Photon pair states	253
6.8	Two-photon interference	260
6.9	Squeezed light	265
6.10	Quantum theory of direct detection	271
6.11	Homodyne detection	278
6.12	The electromagnetic vacuum	284
	References	286
7	Optical generation, attenuation and amplification	288
7.1	Single-mode photon rate equations	289
7.2	Solutions for fixed atomic populations	292
7.3	Single-mode laser theory	297
7.4	Fluctuations in laser light	304
7.5	Travelling-wave attenuation	310
7.6	Travelling-wave amplification	319
7.7	Dynamics of the atom-radiation system	324
7.8	The source-field expression	328
7.9	Emission by a driven atom	331
	References	337
8	Resonance fluorescence and light scattering	339
8.1	The scattering cross-section	340
8.2	Resonance fluorescence	344
8.3	Weak incident beam	348
8.4	Single-atom resonance fluorescence	352
8.5	Quantum jumps	360
8.6	Two-photon cascade emission	365
8.7	The Kramers-Heisenberg formula	371
8.8	Elastic Rayleigh scattering	374
8.9	Inelastic Raman scattering	378
	References	381
9	Nonlinear quantum optics	383
9.1	The nonlinear susceptibility	383
9.2	Electromagnetic field quantization in media	389
9.3	Second-harmonic generation	393
9.4	Parametric down-conversion	398
9.5	Parametric amplification	404
9.6	Self-phase modulation	411
9.7	Single-beam two-photon absorption	417
9.8	Conclusion	425
	References	426
	Index	429