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

TL;DR

This paper introduces a class of time-local, perturbative non-Markovian master equations derived from stochastic Schrödinger equations that guarantee positivity, expanding the tools for studying complex open quantum systems.

Contribution

It presents a novel method for deriving positivity-preserving non-Markovian master equations applicable to a wide range of environments, addressing limitations of previous approximations.

Findings

The new master equations guarantee positivity in non-Markovian dynamics.

Numerical simulations demonstrate the effectiveness of the approach.

The method is applicable to ultrafast quantum processes and strong-coupling systems.

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.