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Quantum Optics$
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John Garrison and Raymond Chiao

Print publication date: 2008

Print ISBN-13: 9780198508861

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780198508861.001.0001

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The master equation

The master equation

(p.538) 18 The master equation
Quantum Optics

J. C. Garrison

R. Y. Chiao

Oxford University Press

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.

Keywords:   quantum Liouville equation, world density operator, sample density operator, master equation, Fokker-Planck equation, Monte Carlo wavefunction, quantum trajectory, quantum state diffusion

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