Entanglement and energy transportation in the central-spin quantum battery

TL;DR

This paper investigates the energy transfer and entanglement in a central-spin quantum battery, revealing a universal inverse relation between capacity and entanglement, and identifying optimal conditions for energy transport efficiency.

Contribution

It introduces the invariant subspace method for analyzing large-scale central-spin quantum batteries and uncovers fundamental relationships between entanglement and energy transfer.

Findings

Universal inverse relationship between capacity and entanglement.

Optimal energy transport occurs when battery and charger sizes are equal.

Energy transport behavior is uniform at certain size scales.

Abstract

Quantum battery exploits the principle of quantum mechanics to transport and store energy. We study the energy transportation of the central-spin quantum battery, which is composed of $N_b$ spins serving as the battery cells, and surrounded by $N_c$ spins serving as the charger cells. We apply the invariant subspace method to solve the dynamics of the central-spin battery with a large number of spins. We establish a universal inverse relationship between the battery capacity and the battery-charger entanglement, which persists in any size of the battery and charger cells. Moreover, we find that when $N_b=N_c$, the central-spin battery has the optimal energy transportation, corresponding to the minimal battery-charger entanglement. Surprisingly, the central-spin battery has a uniform energy transportation behaviors in certain battery-charger scales. Our results reveal a nonmonotonic relationship between the battery-charger size and the energy transportation efficiency, which may provide more insights on designing other types of quantum batteries.