Ergotropy in Quantum Batteries

TL;DR

This paper explores the dynamics of ergotropy in quantum batteries, revealing how coherence, population inversion, and state properties influence energy extraction and charging efficiency, with implications for designing high-performance quantum energy storage.

Contribution

It provides a comprehensive framework for understanding and optimizing ergotropy in quantum batteries, including the roles of coherence, population inversion, and state properties, validated through paradigmatic models.

Findings

Ergotropy varies with population inversion and coherence.

Coherence and participation ratio enhance coherent ergotropy.

Incoherent ergotropy depends on entropy, participation ratio, and energy level order.

Abstract

Ergotropy--a key figure of merit for quantum battery (QB) performance--plays a crucial role. However, the dynamics and physical mechanisms governing ergotropy evolution remain open challenges. Here, we investigate the ergotropy of a general QB model and find that the charging process is accompanied by the variation and inversion of the energy level populations. In the absence of population inversion, the ergotropy is fully consistent with coherent ergotropy; in local and global population inversion, it is determined by both coherent and incoherent ergotropy. Via random sampling of quantum states and Hamiltonians, we show that coherence and the participation ratio enhance coherent ergotropy, whereas incoherent ergotropy--whether enhanced, unchanged, or suppressed--depends on diagonal entropy, the participation ratio, and energy level population ordering. We demonstrate that the ergotropy lower bound is incoherent ergotropy, the upper bound is the QB stored energy, and enhanced QB purity suppresses locked energy and boosts charging efficiency. Furthermore, we use the Tavis-Cummings (TC) and Jaynes-Cummings (JC) batteries as paradigms to validate our findings. Our work elucidates ergotropy underlying mechanisms in general QBs and establishes a rigorous framework for optimizing ergotropy and charging efficiency, paving the way for high-performance quantum energy-storage devices.