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Zeitschrift für Naturforschung A

Dynamical Symmetry Method Investigates the Dissipation and Decoherence of the two-level Jaynes–Cummings Model

Qin-Sheng Zhu, Wei Lai, Da-Lin Wu

Published Aug 20, 2012• 1 citation
Publisher

Abstract

Based on the quantum master equation which describes the dynamical evolution of a two-level atom interacting with one mode of the quantized photon field in a cavity, we have investigated the systemic dissipative and decoherence properties by use of the development algebraic dynamic method for the automatic and non-automatic condition. Furthermore, using the exact solution of the quantum master equation, we have investigated the asymptotic behaviours of the system.

DOI
10.5560/zna.2012-0058

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Based on the quantum master equation which describes the dynamical evolution of a two-level atom interacting with one mode of the quantized photon field in a cavity, we have investigated the systemic dissipative and decoherence properties by use of the development algebraic dynamic method for the automatic and non-automatic condition. Furthermore, using the exact solution of the quantum master equation, we have investigated the asymptotic behaviours of the system.
Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.
The dissipative and decoherence properties of a two-level atom interacting with a squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equation and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solutions and the steady solutions are obtained analytically. The asymptotic behaviour of the solutions is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.
The dissipative and decoherence properties of the two-level atom interacting with the squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schr\\"{o}dinger-like equations and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solution and the steady solution are obtained analytically. The asymptotic behavior of the solution is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.