Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics

TL;DR

This paper extends the pseudomode framework for open quantum systems by allowing non-Hermitian pseudomodes, reducing complexity, enabling efficient simulations, and providing insights into system-environment interactions beyond the weak-coupling limit.

Contribution

It generalizes the pseudomode approach to include non-Hermitian states, decreasing the number of pseudomodes needed and facilitating numerical simulations of non-Markovian dynamics.

Findings

Generalized conditions for master equations with non-Hermitian pseudomodes

Reduced pseudomode count for underdamped environments at finite temperature

Unraveling into quantum jump trajectories for improved numerical methods

Abstract

The pseudomode framework provides an exact description of the dynamics of an open quantum system coupled to a non-Markovian environment. Using this framework, the influence of the environment on the system is studied in an equivalent model, where the open system is coupled to a finite number of unphysical pseudomodes that follow a time-local master equation. Building on the insight that this master equation does not need to conserve the hermiticity of the pseudomode state, we here ask for the most general conditions on the master equation that guarantee the correct reproduction of the system's original dynamics. We demonstrate that our generalized approach decreases the number of pseudomodes that are required to model, for example, underdamped environments at finite temperature. We also provide an unraveling of the master equation into quantum jump trajectories of non-Hermitian states, which further facilitates the utilization of the pseudomode technique for numerical calculations by enabling the use of easily parallelizable Monte Carlo simulations. Finally, we show that pseudomodes, despite their unphysical nature, provide a natural picture in which physical processes, such as the creation of system-bath correlations or the exchange of heat, can be studied. Hence, our results pave the way for future investigations of the system-environment interaction leading to a better understanding of open quantum systems far from the Markovian weak-coupling limit.