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Journal of Modern Optics

Algebraic solution of master equations in quantum optics

K. V. S. Shiv Chaitanya

Published Dec 17, 2010• 6 citations
Publisher

Abstract

The techniques in thermo field dynamics are applied to solve a certain class of master equations associated with su(1,1) × su(1,1) symmetries exactly by an algebraic approach using disentanglement theorem.
DOI
10.1080/09500340.2010.536593

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An SU(1,1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems. The Liouville space formulation, thermo field dynamics, and the disentanglement theorem of SU(1,1) Lie algebra play essential roles in this formulation. In the Liouville space, the time-evolution equation for the state vector of a system is solved algebraically by using the decomposition formulas of SU(1,1) Lie algebra and the thermal state condition of thermo field dynamics. The presented formulation is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron–phonon system. This algebraic formulation gives a systematic treatment for investigating the phenomena in quantum optical systems.