Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

TL;DR

This paper introduces an exact tensor network-based solution for open quantum system dynamics interacting with correlated environments, enabling analytical treatment of complex non-Markovian phenomena.

Contribution

It develops a tensor network formalism that provides an exact Markovian embedding for correlated environment interactions in open quantum systems.

Findings

Exact tensor network solution for correlated environment dynamics

Analytical treatment of two-photon wavepackets and structured states

Derived a time-convolution master equation linking memory kernel and environment correlations

Abstract

Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to analytical treatment for a number of timely problems like the system interaction with two-photon wavepackets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.