Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
8 - Quantum theory of damping – density operator and wave function approach
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
Summary
In many problems in quantum optics, damping plays an important role. These include, for example, the decay of an atom in an excited state to a lower state and the decay of the radiation field inside a cavity with partially transparent mirrors. In general, damping of a system is described by its interaction with a reservoir with a large number of degrees of freedom. We are interested, however, in the evolution of the variables associated with the system only. This requires us to obtain the equations of motion for the system of interest only after tracing over the reservoir variables. There are several different approaches to deal with this problem.
In this chapter, we present a theory of damping based on the density operator in which the reservoir variables are eliminated by using the reduced density operator for the system in the Schrödinger (or interaction) picture. We also present a ‘quantum jump’ approach to damping. In the next chapter, the damping of the system will be considered using the noise operator method in the Heisenberg picture.
An insight into the damping mechanism is obtained by considering the decay of an atom in an excited state inside a cavity. The atom may be considered as a single system coupled to the radiation field inside the cavity. Even in the absence of photons in the cavity, there are quantum fluctuations associated with the vacuum state. As discussed in Chapter 1, the field may be visualized as a large number of harmonic oscillators, one for each mode of the cavity.
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- Chapter
- Information
- Quantum Optics , pp. 248 - 270Publisher: Cambridge University PressPrint publication year: 1997
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