Charging a quantum battery from the Bloch sphere

TL;DR

This paper analyzes how the initial quantum state on the Bloch sphere affects energy storage and power in a simple two-qubit quantum battery, revealing new insights into quantum coherence and thermodynamics.

Contribution

It provides generalized analytical expressions for energy, ergotropy, and capacity depending on the initial Bloch sphere state, highlighting the role of quantum coherences.

Findings

Stored energy and ergotropy depend on initial Bloch angle.

Quantum coherences influence battery capacity and ergotropy.

Charging power and optimal time deviate from classical thermodynamic predictions.

Abstract

We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.