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Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach

Wufu ShiYusui ChenQuanzhen DingTing YuJin Wang
Dec 2022
摘要
Positivity preservation is naturally guaranteed in exact non-Markovian masterequations for open quantum system dynamics. However, in many approximatednon-Markovian master equations, the positivity of the reduced density matrix isnot guaranteed. In this paper, we provide a general class of time-localperturbative and positivity preserving non-Markovian master equations generatedfrom stochastic Schr\"odinger equations, particularly quantum-state-diffusionequations. Our method has an expanded range of applicability for accommodatinga vast variety of non-Markovian environments. We show the positivity preservingmaster equation for a dissipative three-level system coupled to a bosonicenvironment as a particular example of our general result. We illustrate thenumerical simulations with an analysis explaining why the previous approximatednon-Markovian master equations cannot preserve positivity. Our work paves theway for studying the non-Markovian dynamics in ultrafast quantum processes andstrong-coupling systems.
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