Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation

TL;DR

This paper introduces a stochastic unravelling method for a generalized non-Markovian quantum master equation, enabling simulation of complex quantum processes with improved accuracy and comparison to existing methods.

Contribution

It presents a novel stochastic unravelling approach for the generalized Lindblad master equation, extending quantum trajectory methods to non-Markovian dynamics.

Findings

The stochastic unravelling accurately reproduces the exact dynamics.

Numerical results agree well with the TCL projection method.

The approach effectively models a two-state system coupled to a structured environment.

Abstract

Recently a generalized master equation was derived that extends the Lindblad theory to highly non-Markovian quantum processes (H.-P. Breuer, Phys. Rev. A \textbf{75}, 022103 (2007)). We perform a stochastic unravelling of this master equation by considering $n$ random state vectors that satisfy the corresponding stochastic differential equation for a piecewise deterministic process. As an application we consider a two-state system randomly coupled to an environment consisting of two energy bands with finite number of levels. Our numerical results are compared to results obtained from the time-convolutionless (TCL) projection operator method using correlated projection superoperators and the exact solution of the Schr\"{o}dinger equation for this system.