Collision-model-based approach to non-Markovian quantum dynamics

TL;DR

This paper introduces a collision-model framework for non-Markovian quantum dynamics, incorporating bath memory via inter-ancillary collisions, and derives a master equation that accurately describes complex quantum systems.

Contribution

It develops a microscopic collision model with bath memory, deriving a general master equation that captures non-Markovian effects while ensuring complete positivity.

Findings

The model interpolates between Markovian and strongly non-Markovian dynamics.

The derived master equation is unconditionally completely positive and trace-preserving.

Application to an atom in a dissipative cavity shows improved accuracy over existing models.

Abstract

We present a theoretical framework to tackle quantum non-Markovian dynamics based on a microscopic collision model (CM), where the bath consists of a large collection of initially uncorrelated ancillas. Unlike standard memoryless CMs, we endow the bath with memory by introducing inter-ancillary collisions between next system-ancilla interactions. Our model interpolates between a fully Markovian dynamics and the continuous interaction of the system with a single ancilla, i.e., a strongly non-Markovian process. We show that in the continuos limit one can derive a general master equation, which while keeping such features is guaranteed to describe an unconditionally completely positive and trace-preserving dynamics. We apply our theory to an atom in a dissipative cavity for a Lorentzian spectral density of bath modes, a dynamics which can be exactly solved. The predicted evolution shows a significant improvement in approaching the exact solution with respect to two well-known memory-kernel master equations.