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.
Highlights
A quantum thermal machine is an open quantum system coupled to thermal reservoirs
We investigate how the state of the quantum thermal machine relaxes towards its steady state, i.e., we characterize the dynamics through the presence or not of oscillations and determine the damping rates associated with the different decay channels
Focusing on the non-Hermitian physics induced by the dissipators to the environments, we derived a number of Liouvillian exceptional points (EPs) of different orders for this system for experimentally valid range of parameters
Summary
A quantum thermal machine is an open quantum system coupled to thermal reservoirs. By judiciously designing the machine, one can take advantage of the energy exchange with the reservoirs in order to perform a thermodynamic task, such as cooling or producing work [1,2,3,4], or to perform a genuine quantum task, such as creating quantum correlations [5,6,7,8]. Open questions concern the search for Hamiltonian and Liouvillian EPs in state-of-the-art physical platforms and their signatures [42,43,44,45,46,47,48,49,50,51,52,53], especially in the quantum regime. We uncover a signature of EPs in the long-time dynamics, in the form of critical decay towards the steady state, in analogy to critical damping in a harmonic oscillator These results broaden the class of systems exhibiting EPs and opens new routes for controlling the quantum dynamics of nanoscale thermal machines.
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