Performance limits of multilevel and multipartite quantum heat machines

TL;DR

This paper investigates the fundamental performance limits of quantum heat machines based on N-level systems with degenerate excited states, highlighting how degeneracy and dipole orientations influence efficiency and power.

Contribution

It provides a general theoretical framework for N-level quantum heat machines, analyzing the effects of level degeneracy and dipole alignment on their thermodynamic performance.

Findings

Degeneracy enhances heat currents and power output.

Efficiency remains bounded by Carnot limit, unaffected by degeneracy.

Dipole orientation affects steady-state coherence and performance.

Abstract

We present the general theory of a quantum heat machine based on an $N$-level system (working medium) whose $N-1$ excited levels are degenerate, a prerequisite for steady-state interlevel coherence. Our goal is to find out: To what extent is coherence in the working medium an asset for heat machines? The performance bounds of such a machine are common to (reciprocating) cycles that consist of consecutive strokes and continuous cycles wherein the periodically driven system is constantly coupled to cold and hot heat baths. Intriguingly, we find that the machine's performance strongly depends on the relative orientations of the transition-dipole vectors in the system. Perfectly aligned (parallel) transition dipoles allow for steady-state coherence effects, but also give rise to dark states, which hinder steady-state thermalization and thus reduce the machine's performance. Similar thermodynamic properties hold for $N$ two-level atoms conforming to the Dicke model. We conclude that level degeneracy, but not necessarily coherence, is a thermodynamic resource, equally enhancing the heat currents and the power output of the heat machine. By contrast, the efficiency remains unaltered by this degeneracy and adheres to the Carnot bound.