Collision model for non-Markovian quantum dynamics

TL;DR

This paper introduces a collision model framework for simulating non-Markovian quantum dynamics, enabling the study of quantum memory effects and embedding non-Markovian behavior into Markovian models.

Contribution

It proposes a novel collision model allowing environmental interactions to capture non-Markovian effects and demonstrates embedding these models into Markovian dynamics.

Findings

Successfully models non-Markovian amplitude damping of a qubit

Recovers known spontaneous decay results in the continuous limit

Provides a framework for studying quantum memory effects

Abstract

We study the applicability of collisional models for non-Markovian dynamics of open quantum systems. By allowing interactions between the separate environmental degrees of freedom in between collisions we are able to construct a collision model that allows to study quantum memory effects in open system dynamics. We also discuss the possibility to embed non-Markovian collision model dynamics into Markovian collision model dynamics in an extended state space. As a concrete example we show how using the proposed class of collision models we can discretely model non- Markovian amplitude damping of a qubit. In the time-continuous limit, we obtain the well-known results for spontaneous decay of a two level system in to a structured zero-temperature reservoir