Optimal energy storage and collective charging speedup in the central-spin quantum battery

TL;DR

This paper analytically investigates a central-spin quantum battery model, revealing conditions for optimal energy storage and demonstrating collective charging speedup, with implications for quantum energy storage efficiency.

Contribution

It introduces an analytical framework for central-spin quantum batteries, identifying scenarios for optimal storage and quantifying collective charging speedup.

Findings

Optimal energy storage conditions identified for various parameter regimes.

Collective charging speedup scales as N_b in certain cases.

Asymptotic optimal storage with N_b = m = N_c achieved, with a speedup scaling as N_b^{0.8264}.

Abstract

Quantum batteries (QBs) exploit principles of quantum mechanics to accelerate the charging process and aim to achieve optimal energy storage. However, analytical results for investigating these problems remain lacking due to the challenges associated with nonequilibrium dynamics. In this work, we analytically investigate a central-spin QB model in which $N_b$ spin-1/2 battery cells interact with $N_c$ spin-1/2 charger units, using $m$ initially excited charger units as a resource. By employing the invariant subspace method and the shifted Holstein-Primakoff transformation, we identify four scenarios in which optimal energy storage can be achieved: (i) $N_b\!\ll\!m\!\ll\!N_c$; (ii) $m\!\ll\!N_b\!\ll\!N_c$; (iii) $m\!\ll\!N_c\!\ll\!N_b$; and (iv) $N_b\!\ll\!m\!=\!kN_c$ [$k\!\in\!(0,1)$]. In these cases, optimal storage is ensured by the SU(2) symmetry emerging from the charging dynamics. The first three cases map the central-spin QB to different Tavis-Cummings (TC) QBs, while the fourth corresponds to the non-TC limit. We analytically determine the charging time and demonstrate that in the fully charging cases (i) and (iv), the collective charging exhibits an $N_b$-fold enhancement in speedup compared to the parallel charging scheme. Additionally, we numerically observe a unified charging behavior when $m\!=\!N_c$, showing that asymptotically optimal energy storage is possible when $N_b\!=\!m\!=\!N_c$. In this case, we find a collective charging enhancement scaling as $N_b^{0.8264}$. The origin of the collective charging advantage in central-spin quantum batteries is also analyzed through the quantum speed limit and a multipartite entanglement witness. Our results highlight the crucial role of dynamically emergent SU(2) symmetry in providing an analytical understanding of non-equilibrium charging dynamics in QBs.