Book contents
- Frontmatter
- Contents
- Preface
- 1 Foundations of quantum statistical mechanics
- 2 Elementary examples
- 3 Quantum statistical master equation
- 4 Quantum kinetic equations
- 5 Quantum irreversibility
- 6 Entropy and dissipation: the microscopic theory
- 7 Global equilibrium: thermostatics and the microcanonical ensemble
- 8 Bose–Einstein ideal gas condensation
- 9 Scaling, renormalization and the Ising model
- 10 Relativistic covariant statistical mechanics of many particles
- 11 Quantum optics and damping
- 12 Entanglements
- 13 Quantum measurement and irreversibility
- 14 Quantum Langevin equation and quantum Brownian motion
- 15 Linear response: fluctuation and dissipation theorems
- 16 Time-dependent quantum Green's functions
- 17 Decay scattering
- 18 Quantum statistical mechanics, extended
- 19 Quantum transport with tunneling and reservoir ballistic transport
- 20 Black hole thermodynamics
- A Problems
- Index
- References
11 - Quantum optics and damping
Published online by Cambridge University Press: 05 August 2015
- Frontmatter
- Contents
- Preface
- 1 Foundations of quantum statistical mechanics
- 2 Elementary examples
- 3 Quantum statistical master equation
- 4 Quantum kinetic equations
- 5 Quantum irreversibility
- 6 Entropy and dissipation: the microscopic theory
- 7 Global equilibrium: thermostatics and the microcanonical ensemble
- 8 Bose–Einstein ideal gas condensation
- 9 Scaling, renormalization and the Ising model
- 10 Relativistic covariant statistical mechanics of many particles
- 11 Quantum optics and damping
- 12 Entanglements
- 13 Quantum measurement and irreversibility
- 14 Quantum Langevin equation and quantum Brownian motion
- 15 Linear response: fluctuation and dissipation theorems
- 16 Time-dependent quantum Green's functions
- 17 Decay scattering
- 18 Quantum statistical mechanics, extended
- 19 Quantum transport with tunneling and reservoir ballistic transport
- 20 Black hole thermodynamics
- A Problems
- Index
- References
Summary
Introduction
In this chapter we will turn to the arena of quantum optics for illustrative examples of the use of the master equation discussed in Chapters 3 and 6. In fact, quantum optics examples have already been utilized in Chapter 2 as introduction to the density matrix. The principal focus here will be quantum damping in these systems, that is, the damping effect on an atom in interaction with the electromagnetic field as a reservoir. Damping is discussed extensively in Chapter 17 in connection with decay-scattering systems. For this system general phase space distribution functions will be reexamined. To some degree, this has already been done in Chapter 2 with the introduction of the Glauber–Sudarshan P (α a*) function. The micromaser will be discussed as a modern and interesting example of the dynamic interaction of an atom with an electromagnetic cavity not in equilibrium. For use of the student, an appendix to this chapter will briefly review the quantization of the free electromagnetic field and its atomic interaction.
There is no possibility of reviewing this extensive and growing field here. Our desire in this chapter is to connect the general topics of this book to this example. The books of Louisell (1973) and Scully and Zubairy (1997) are excellent. We are also indebted to the work of Nussenzweig, Schleich, and Mandel and Wolf (Nussenzweig, 1973; Mandel and Wolf, 1995; Schleich, 2001). We also recall the fine early introduction to this topic by Agarwal (1973).
Atomic damping: atomic master equation
In this section we shall consider the so-called quantum optics master equation for the reduced atomic density operator, ρA (t), in the Born approximation. The elements of this derivation have already been discussed in Chapter 3 with the derivation of the Pauli equation for 〈α|ρA |α〉. Here the generalization to off-diagonal contributions only adds complication.
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- Quantum Statistical Mechanics , pp. 199 - 220Publisher: Cambridge University PressPrint publication year: 2009