Efficiency at maximum power of a quantum Carnot engine with temperature tunable baths

TL;DR

This paper studies the efficiency at maximum power of a quantum Carnot engine with tunable baths, proposing bounds and analyzing a minimal model with a two-level spin, relevant for practical quantum thermodynamics.

Contribution

It generalizes bounds for efficiency at maximum power to temperature tunable baths and analyzes a minimal quantum heat engine model with practical relevance.

Findings

Efficiency at maximum power is constrained by generalized bounds.

A two-level spin model mimics low dissipation quantum engines.

The efficiency follows a generalized Curzon-Ahlborn form under optimal conditions.

Abstract

We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine model with a two-level spin as the working medium. It mimics a low dissipation engine as confirmed by finite time thermodynamic optimization results. The so-obtained EMP, being constrained by the generalized bounds, is well described by a generalized Curzon- Ahlborn efficiency as consequences of a left/right symmetry for a rate constant and low dissipations. Intriguing features of this minimal heat engine under optimal power output are also demonstrated.