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

• URL: http://arxiv.org/abs/2212.13362v2
• Date: Fri, 30 Dec 2022 16:57:44 GMT
• Title: Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach
• Authors: Wufu Shi, Yusui Chen, Quanzhen Ding, Ting Yu and Jin Wang
• Abstract summary: Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. We provide a general class of timelocal perturbative and positivity preserving non-Markovian master equations. Our work paves the way for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.
• Score: 9.313696763561044
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local perturbative and positivity preserving non-Markovian master equations generated from stochastic Schr\"odinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a vast variety of non-Markovian environments. We show the positivity preserving master equation for a dissipative three-level system coupled to a bosonic environment as a particular example of our general result. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot preserve positivity. Our work paves the way for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.

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