Signatures of Liouvillian exceptional points in a quantum thermal machine

TL;DR

This paper investigates the dynamics of quantum thermal machines modeled as non-Hermitian systems, revealing the presence of Liouvillian exceptional points that influence their decay behavior and can be exploited for control in solid-state platforms.

Contribution

It provides a general analytical framework for the time-dependent dynamics of quantum thermal machines by deriving their Liouvillian spectrum, highlighting the role of exceptional points in their behavior.

Findings

Identification of Liouvillian exceptional points in quantum thermal machines.

Discovery of a third-order exceptional point affecting decay dynamics.

Potential for dynamical control using exceptional points in solid-state devices.

Abstract

Viewing a quantum thermal machine as a non-Hermitian quantum system, we characterize in full generality its analytical time-dependent dynamics by deriving the spectrum of its non-Hermitian Liouvillian for an arbitrary initial state. We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters, in particular a third-dorder exceptional point that leaves signatures both in short and long-time regimes. Remarkably, we demonstrate that this EP corresponds to a regime of critical decay for the quantum thermal machine towards its steady state, bearing a striking resemblance with a critically damped harmonic oscillator. These results open up exciting possibilities for the precise dynamical control of quantum thermal machines exploiting exceptional points from non-Hermitian physics and are amenable to state-of-the-art solid-state platforms such as semiconducting and superconducting devices.