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arXiv · 2212.13362

Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schrödinger Equation Approach

Wufu Shi·Yusui Chen·Quanzhen Ding·Jin Wang·Ting Yu
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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 Schrodinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.

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Wufu Shi, Yusui Chen, Quanzhen Ding, Jin Wang, Ting Yu. 2023-03-14. Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schrödinger Equation Approach. https://doi.org/10.1103/physreva.109.022203

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