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arXiv:0810.2337 · Physical Review E

Non-Markovian quantum jump with generalized Lindblad master equation

X. L. Huang, Hongchang Sun, X. X. Yi

Published Oct 6, 2008• 19 citations
arXivHTMLPDF

Abstract

The Monte Carlo wave function method or the quantum-trajectory-jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. We extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method is also discussed.

DOI
10.1103/physreve.78.041107

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The Monte Carlo wave function method or the quantum-trajectory-jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. We extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method is also discussed.
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Open quantum systems are ubiquitous in nature and central to quantum technologies. A common description of their dynamics is given by the celebrated Lindblad master equation, which can be generalized to the non-Markovian scenario. In this work, we introduce the non-Markovian ensemble propagation (NMEP) method, which extends the Monte Carlo wave-function (MCWF) method to the non-Markovian case in a simple and general manner. We demonstrate its accuracy and effectiveness in a selection of examples, and compare the results with either analytic expressions or direct numerical integration of the master equation.
Open quantum systems are ubiquitous in nature and central to quantum technologies. A common description of their dynamics is given by the celebrated Lindblad master equation, which can be generalized to the non-Markovian scenario. In this work, we introduce the non-Markovian ensemble propagation (NMEP) method, which extends the Monte Carlo wave-function (MCWF) method to the non-Markovian case in a simple and general manner. We demonstrate its accuracy and effectiveness in a selection of examples, and compare the results with either analytic expressions or direct numerical integration of the master equation.
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The Monte Carlo wave-function method has recently proved to be an efficient tool in the analysis of linear dissipative quantum systems, i.e., systems with linear equations of motion for their density matrix. We generalize this method to systems with nonlinear master equations of a parametrized Lindblad form, which includes master equations obtained by Hartree-Fock approximations. Convergence properties of the algorithm are discussed in detail. The method is illustrated by a numerical analysis of the bosonic enhancement of laser cooling of trapped particles. \textcopyright{} 1996 The American Physical Society.
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