*Serge Haroche and Jean-Michel Raimond*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198509141
- eISBN:
- 9780191708626
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509141.003.0004
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter presents the general relaxation theory which describes the dynamical evolution of an open system A coupled to a large environment E. Section 4.1 reviews the main properties of the ...
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This chapter presents the general relaxation theory which describes the dynamical evolution of an open system A coupled to a large environment E. Section 4.1 reviews the main properties of the density matrix, including ‘density matrix purification’. Section 4.2 describes a general representation of a ‘quantum process’, mapping a density matrix onto another one. With a few simple and reasonable hypotheses on E, Section 4.3 casts the master equation under the generic Lindblad form. Section 4.4 introduces the Monte Carlo description of quantum relaxation. Section 4.5 considers a cavity mode resonantly coupled to a single two-level atom and describes how the Rabi oscillation phenomenon is altered by atomic and cavity relaxation. In Section 4.6, the two-level atoms are coupled sequentially to the spring, providing a simple model of a ‘micromaser’. Finally, in Section 4.7, the spins are simultaneously coupled to the spring, realizing a simple model for co-operative emission phenomena.Less

This chapter presents the general relaxation theory which describes the dynamical evolution of an open system *A* coupled to a large environment *E*. Section 4.1 reviews the main properties of the density matrix, including ‘density matrix purification’. Section 4.2 describes a general representation of a ‘quantum process’, mapping a density matrix onto another one. With a few simple and reasonable hypotheses on E, Section 4.3 casts the master equation under the generic Lindblad form. Section 4.4 introduces the Monte Carlo description of quantum relaxation. Section 4.5 considers a cavity mode resonantly coupled to a single two-level atom and describes how the Rabi oscillation phenomenon is altered by atomic and cavity relaxation. In Section 4.6, the two-level atoms are coupled sequentially to the spring, providing a simple model of a ‘micromaser’. Finally, in Section 4.7, the spins are simultaneously coupled to the spring, realizing a simple model for co-operative emission phenomena.

*J. C. Garrison and R. Y. Chiao*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198508861
- eISBN:
- 9780191708640
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508861.003.0019
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter examines the evolution of an open system — the sample — with the quantum Liouville equation for the world density operator. The fundamental approximation is that the action of the sample ...
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This chapter examines the evolution of an open system — the sample — with the quantum Liouville equation for the world density operator. The fundamental approximation is that the action of the sample on the environment is negligible compared to the action of the environment on the sample. This leads to the master equation for the (reduced) sample density operator. Photons in a cavity and a two-level atom are presented as examples. The P-function representation of the sample density operator yields the Fokker-Planck equation. This is used to show the robustness of coherent states, and to describe a driven mode in a lossy cavity. The discussion next turns to quantum jumps and their experimental observation. Quantum jumps are related to the master equations by means of the Monte Carlo wavefunction algorithm, quantum trajectories, and quantum state diffusion.Less

This chapter examines the evolution of an open system — the sample — with the quantum Liouville equation for the world density operator. The fundamental approximation is that the action of the sample on the environment is negligible compared to the action of the environment on the sample. This leads to the master equation for the (reduced) sample density operator. Photons in a cavity and a two-level atom are presented as examples. The P-function representation of the sample density operator yields the Fokker-Planck equation. This is used to show the robustness of coherent states, and to describe a driven mode in a lossy cavity. The discussion next turns to quantum jumps and their experimental observation. Quantum jumps are related to the master equations by means of the Monte Carlo wavefunction algorithm, quantum trajectories, and quantum state diffusion.