Introduction to Modern Quantum Optics

by Peng, Jin-Sheng; Li, Gao-Xiang

• ISBN13: 9789810234485
• ISBN10: 9810234481
• Edition: 1st
• Format: Hardcover
• Copyright: 1998-09-01
• Publisher: World Scientific Pub Co Inc

Summary

Based on lectures in quantum optics for graduate students, on research publications over the past few years, & on the latest achievements in the field of quantum optics. Text is dedicated to the main contents of quantum optics according to the quantum properties of both atoms & radiation fields in the atom-field coupling system.

Table of Contents

Preface	v
PART I. Theory of the interaction between atom and radiation field	3	(132)
Chapter 1. Three pictures in quantum mechanics	3	(22)
1.1. The Schrodinger picture	3	(5)
1.2. The Heisenberg picture	8	(3)
1.3. The interaction picture	11	(4)
1.3.1. Equation of motion in the interaction picture	11	(2)
1.3.2. A formal solution of the state vector XXX (t) by the perturbation theory	13	(2)
1.4. The density operator	15	(10)
1.4.1. Density operator and its general properties	16	(4)
1.4.2. Solution of the equation of motion for the density operator	20	(5)
Chapter 2. Two-level atom and the optical Bloch equation	25	(12)
2.1. Two-level atom	25	(1)
2.2. Hamiltonian of a two-level atom interacting with an electromagnetic field	26	(2)
2.3. The optical Bloch equation	28	(3)
2.4. Description of the dynamical behavior of a two-level atom interacting with the radiation field by the density matrix	31	(6)
2.4.1. Density matrix equation describing a two-level atom without decay	32	(2)
2.4.2. Density matrix equation of a two-level atom with decay	34	(3)
Chapter 3. Quantized description of radiation field	37	(40)
3.1. Classical description of the electromagnetic field in vacuum	37	(5)
3.2. Quantization of the radiation field	42	(6)
3.2.1. Quantization of the electromagnetic field	42	(3)
3.2.2. Momentum and spin of the photon	45	(3)
3.3. State functions describing the light field	48	(29)
3.3.1. Photon-number states	48	(4)
3.3.2. The coherent states of light	52	(8)
3.3.3. The phase operators and the phase states	60	(12)
3.3.4. Chaotic states of light	72	(5)
Chapter 4. Dicke Hamiltonian and Jaynes-Cummings Model	77	(16)
4.1. Dicke Hamiltonian of an atom interacting with the radiation field	77	(5)
4.2. Spontaneous emission of an excited atom	82	(5)
4.3. The Jaynes-Cummings model	87	(6)
Chapter 5. Quantum theory of a small system coupled to a reservoir	93	(42)
5.1. Classical Langevin equation and Fokker-Planck equation	93	(14)
5.1.1. Langevin equation	94	(4)
5.1.2. Fokker-Planck equation	98	(9)
5.2. Master equation for a quantum harmonic oscillator and a two-level atom	107	(11)
5.2.1. Master equation for a quantum harmonic oscillator	108	(8)
5.2.2. Master equation for a two-level atom coupled to a bath field	116	(2)
5.3. Characteristic function and the quasi-probability distribution for the quantum harmonic oscillator	118	(17)
5.3.1. Normal ordering representation	119	(3)
5.3.2. Anti-normal ordering representation	122	(3)
5.3.3. Symmetric ordering representation	125	(10)
PART II. The quantum properties of light	135	(198)
Chapter 6. Coherence of light	135	(25)
6.1. Classical coherence of light	135	(10)
6.1.1. Temporal coherence of light	135	(2)
6.1.2. Spatial coherence of light	137	(1)
6.1.3. The first-order correlation function	138	(4)
6.1.4. The higher-order correlation function	142	(3)
6.2. Quantum theory of the coherence of light	145	(15)
6.2.1. Quantum correlation functions	145	(4)
6.2.2. Bunching and antibunching effects of light	149	(6)
6.2.3. Intermode correlation property for the two-mode field	155	(5)
Chapter 7. Squeezed states of light	160	(40)
7.1. Squeezed states of a single-mode field	160	(17)
7.1.1. Squeezed coherent states	160	(16)
7.1.2. Squeezed vacuum field	176	(1)
7.2. Squeezed states of a two-mode radiation field	177	(8)
7.3. Higher-order Squeezing of a radiation field and the amplitude square squeezing	185	(5)
7.3.1. Higher-order squeezing of a radiation field	185	(3)
7.3.2. Amplitude Square Squeezing	188	(1)
7.3.3. Independence of the different definitions of the squeezing for the radiation field	189	(1)
7.4. Squeezing of light in the Jaynes-Cummings model	190	(10)
Chapter 8. Resonance fluorescence	200	(47)
8.1. Resonance fluorescence distribution of a two-level atom	200	(22)
8.1.1. Dressed canonical transformation	200	(6)
8.1.2. Spectral distribution of the resonance fluorescence of a two-level atom	206	(3)
8.1.3. Linewidth of the fluorescence spectrum	209	(5)
8.1.4. Intensity distribution of the resonance fluorescence spectrum	214	(8)
8.2. Resonance fluorescence spectra of a three-level atom	222	(14)
8.2.1. Hamiltonian of a three-level atom under the interaction of a bimodal field	222	(2)
8.2.2. Resonance fluorescence spectrum of a three-level atom interacting with a strong and a weak monochromatic laser field	224	(6)
8.2.3. Resonance fluorescence spectral distribution of a three-level atom driven by two strong laser fields	230	(6)
8.3. Single-atom resonance fluorescence described by the density matrix theory	236	(11)
Chapter 9. Superfluorescence	247	(40)
9.1. Elementary features of superfluorescence	247	(4)
9.2. Quasi-classical description of superfluorescence	251	(7)
9.3. Quantum theoretical description of superfluorescence	258	(18)
9.3.1. Heisenberg equation of the system	258	(5)
9.3.2. Dicke model for superfluorescence	263	(5)
9.3.3. Quantum statistical properties of superfluorescence	268	(8)
9.4. Superfluorescent beats	276	(11)
9.4.1. Basic characteristics of the superfluorescent beats	276	(2)
9.4.2. Superfluorescent beats in the Dicke model	278	(9)
Chapter 10. Optical Bistability	287	(18)
10.1. Basic characteristics and the production mechanism of optical bistability	287	(7)
10.2. Quantum description of the dispersive optical bistability	294	(11)
10.2.1. Hamiltonian describing the optical bistability system	295	(2)
10.2.2. Optical bistability properties of the system	297	(8)
Chapter 11. Effects of virtual photon processes	305	(28)
11.1. Relation between the Lamb shift of a Hydrogen atom and the virtual photon field	305	(6)
11.2. Influence of the virtual photon field on the phase fluctuation of the radiation field	311	(8)
11.2.1. Time evolution of the phase operator in the atom-field coupling system with the rotating-wave approximation	311	(4)
11.2.2. Time evolution of the phase operator without the rotating-wave approximation	315	(4)
11.3. Influences of the virtual photon processes on the squeezing of light	319	(14)
11.3.1. Squeezing of the field in the two-photon Jaynes-Cummings model with the rotating-wave approximation	320	(3)
11.3.2. Influences of the virtual photon processes on the squeezing of light	323	(10)
PART III. Quantum properties of atomic behavior under the interaction of a radiation field	333	(226)
Chapter 12. Collapses and revivals of atomic Populations	333	(28)
12.1. Time evolution of the atomic operator of a two-level atom under the interaction of a classical electromagnetic field	333	(3)
12.2.1. Time development of atomic operators under the interaction of the field in a number state XXX	337	(1)
12.2.2. Periodic collapses and revivals of the atom under the interaction of a coherent field	338	(9)
12.3. Periodic collapses and revivals of the atom in the two-photon Jaynes-Cummings model	347	(4)
12.4. Time evolution of the atomic operators for a three-level atom interacting with a single-mode field	351	(10)
12.4.1. Time evolution of the state vector of the system	351	(10)
12.4.2. Periodic collapses and revivals of the atomic populations	354	(7)
Chapter 13. Squeezing effects of the atomic operators	361	(21)
13.1. Definition of the atomic operator squeezing	361	(4)
13.2. Squeezing of atomic operators in the two-photon Jaynes-Cummings model	365	(12)
13.2.1. Squeezing of atomic operators in the vacuum field	367	(5)
13.2.2. Squeezing of atomic operators in the superposition state field	372	(3)
13.2.3. Squeezing of atomic operators in the coherent state field	375	(2)
13.3. Squeezing of atomic operators in the resonace flourescence system	377	(5)
Chapter 14. Coherent trapping of the atomic population	382	(19)
14.1. Atomic population coherent trapping and phase properties in the system of a V-configuration three-level atom interacting with a bimodal field	382	(10)
14.1.1. Time evolution of the state vector of the system	383	(2)
14.1.2. Time evolution of the phase operator in the atom-field coupling system	385	(3)
14.1.3. Coherent trapping of the atomic population	388	(4)
14.2. Coherent trapping of the atomic population for a V-configuration three-level atom driven by a classical field in a heat bath	392	(9)
14.2.1. Time evolution of the reduced density matrix XXX of the atom	393	(3)
14.2.2. Steady-state behavior and the coherent trapping of the atomic populations	396	(5)
Chapter 15. Quantum characteristics of a two-atom system under the interaction of the radiation field	401	(39)
15.1. Hamiltonian of a two-atom system with the dipole-dipole interaction	401	(8)
15.1.1. Hamiltonian of the electric dipole-dipole interaction between two atoms	402	(1)
15.1.2. Hamiltonian of a two-atom system with the dipole-dipole interaction induced by the fluctuations of the vacuum field	403	(6)
15.2. Quantum characteristics of the two-atom coupling system under the interaction of a week field	409	(11)
15.2.1. Time evolution of the atomic population inversion of a two-atom system	411	(5)
15.2.2. Influence of the dipole-dipole interaction on the squeezing of atomic operators	416	(4)
15.3. Periodic collapases and revivals and the coherent population trapping in the two-atom system under the interaction of a coherent field	420	(20)
15.3.1. Periodic collapses and revivals of atomic populations in the two-atom system	424	(7)
15.3.2. Atomic population coherent trapping in the two-atom coupling system	431	(9)
Chapter 16. Autoionization of the atom in a laser field	440	(32)
16.1. Autoionization of the atom in a weak laser field	440	(10)
16.2. Autoionization of the atom under the interaction of a strong laser field	450	(7)
16.3. Above threshold ionization of the atom in a strong laser field	457	(15)
16.3.1. Influences of the second-order ionization processes on the low-energy photoelectron spectrum	464	(2)
16.3.2. Higher-energy photoelectron spectrum and the peak switching effect	466	(6)
Chapter 17. Motion of the atom in a laser field	472	(49)
17.1. Atomic diffraction and deflection in a standing-wave field	472	(18)
17.1.1. State function of the system of an atom interacting with a standing-wave field	472	(7)
17.1.2. Diffraction of the atom under the interaction of a laser field	479	(8)
17.1.3. Deflection of the atom in a standing wave field	487	(3)
17.2. Force on an atom exerted by the radiation field	490	(31)
17.2.1. Quasi-classical description of the radiation force	492	(9)
17.2.2. Description of the radiative dipole force by means of the dressed state method	501	(20)
Chapter 18. Laser cooling	521	(38)
18.1. Decelerating the motion of atoms by use of a laser field	521	(3)
18.2. Quantum theoretical description of the laser cooling	524	(20)
18.2.1. Hamiltonian describing the system of a polarization laser field interacting with a quasi-two-level atom	524	(5)
18.2.2. Time evolution of the density matrix elements of the atomic internal states	529	(6)
18.2.3. Radiation force acting on the atom by the laser field	535	(5)
18.2.4. Physical mechanism of the laser cooling	540	(4)
18.3. Limited temperature of the laser cooling	544	(15)
18.3.1. Atomic momentum diffusion in a laser field	544	(8)
18.3.2. Equilibrium temperature of the laser cooling	552	(2)
18.3.3. Laser cooling below the one-photon recoil energy by the velocity-selective coherent population trapping	554	(5)
Index	559