Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space

TL;DR

This paper introduces a tensor network approach to simulate non-Markovian quantum systems interacting with two structured reservoirs, capturing complex feedback and memory effects with high efficiency.

Contribution

It develops a numerically exact tensor network method combining continuous and discrete memory effects in Liouville space for non-Markovian quantum dynamics.

Findings

Demonstrates long-lived population trapping in a two-level system

Reveals inter-reservoir correlations due to feedback effects

Achieves polynomial efficiency in simulating complex quantum interactions

Abstract

Based on tensor network realizations of path integrals reducing exponential memory scaling to polynomial efficiency and a Liouville space implementation of a time-discrete quantum memory, we investigate a quantum system simultaneously exposed to two structured reservoirs. For this purpose, we employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian dynamical interplay between discrete photonic feedback and structured acoustic phonon modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.