Pseudo-thermalization in driven-dissipative non-Markovian open quantum systems

TL;DR

This paper explores how driven-dissipative quantum systems coupled to non-Markovian reservoirs can exhibit emergent thermal behavior, satisfying fluctuation-dissipation relations despite being out of equilibrium, with implications for quantum optics experiments.

Contribution

It provides an exactly solvable model demonstrating pseudo-thermalization in non-Markovian open quantum systems and analyzes conditions for its occurrence across energy scales.

Findings

Thermal behavior appears at low-energy excitations for generic non-Markovian reservoirs.

Pseudo-thermalization can occur at all energy scales when reservoirs satisfy Kennard-Stepanov relation.

Saturable pumping or dispersive environments disrupt the pseudo-thermalization effect.

Abstract

We investigate a `pseudo thermalization' effect, where an open quantum system coupled to several non-Markovian reservoirs presents an emergent thermal behaviour in spite of its coupling to a non-equilibrated environment. The thermal behaviour is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudo-thermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in exciton-polariton low temperature experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudo-thermalization effect.