Ergotropy from coherences in an open quantum system

TL;DR

This paper demonstrates that steady states of an open quantum system with multiple qubits can contain coherences that enable work extraction, even without population inversion, suggesting a way to design dissipative quantum batteries.

Contribution

It analytically shows the presence of ergotropy in steady states of multi-qubit systems coupled to a thermal bath, linking coherence to work extraction in open quantum systems.

Findings

Steady states can have non-zero ergotropy due to coherences.

Work can be extracted without population inversion.

Ergotropy per energy approaches the $l_1$ coherence norm at high temperature.

Abstract

We show that it is possible to have non-zero ergotropy in the steady-states of an open quantum system consisting of qubits that are collectively coupled to a thermal bath at a finite temperature. The dynamics of our model leads the qubits into a steady-state that has coherences in the energy eigenbasis when the number of qubits in the system is more than one. We observe that even though the system do not have inverted populations, it is possible to extract work from the coherences and analytically show that in the high temperature limit, ergotropy per unit energy is equal to the $l_1$ norm of coherence for the two qubit case. Further, we analyze the scaling of coherence and ergotropy as a function of the number of qubits in the system for different initial states. Our results suggest that one can design a quantum battery that is charged by a dissipative thermal bath in the weak coupling regime.