Open system dynamics with non-Markovian quantum jumps

TL;DR

This paper introduces a non-Markovian quantum jump (NMQJ) method that extends the Monte Carlo Wave Function approach to non-Markovian systems, accurately modeling memory effects and preserving physical probabilities.

Contribution

The NMQJ approach generalizes the Markovian MCWF method to non-Markovian dynamics, ensuring positive jump probabilities and incorporating memory effects within the physical Hilbert space.

Findings

NMQJ accurately models non-Markovian memory effects.

The method preserves probabilities and state norms exactly.

It resolves negative jump probabilities in non-Markovian regimes.

Abstract

We discuss in detail how non-Markovian open system dynamics can be described in terms of quantum jumps [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. Our results demonstrate that it is possible to have a jump description contained in the physical Hilbert space of the reduced system. The developed non-Markovian quantum jump (NMQJ) approach is a generalization of the Markovian Monte Carlo Wave Function (MCWF) method into the non-Markovian regime. The method conserves both the probabilities in the density matrix and the norms of the state vectors exactly, and sheds new light on non-Markovian dynamics. The dynamics of the pure state ensemble illustrates how local-in-time master equation can describe memory effects and how the current state of the system carries information on its earlier state. Our approach solves the problem of negative jump probabilities of the Markovian MCWF method in the non-Markovian regime by defining the corresponding jump process with positive probability. The results demonstrate that in the theoretical description of non-Markovian open systems, there occurs quantum jumps which recreate seemingly lost superpositions due to the memory.