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arXiv:2208.10190 · Physical Review Research

Scaling of energy and power in a large quantum battery-charger model

Lei Gao, Chen Cheng, Wenbin He, Rubem Mondaini, Xi-Wen Guan, Hai‐Qing Lin

Published Nov 30, 2022• 22 citations
arXivHTMLPDF

Abstract

We investigate a multiqubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy ${E}_{B}(t)$ and power ${P}_{B}(t)$, and their maximum values ${E}_{B}^{\mathrm{max}}$ and ${P}_{B}^{\mathrm{max}}$, of the battery part by means of the antiferromagnetic Holstein-Primakoff transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of ${P}_{B}^{\mathrm{max}}$ ensues. By further combining these with the ones obtained via exact diagonalization, we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10 000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with a growing number of charger qubits or when both parts simultaneously grow, we classify the system size scalings of ${E}_{B}^{\mathrm{max}}$ and ${P}_{B}^{\mathrm{max}}$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of ${P}_{B}^{\mathrm{max}}$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings.

DOI
10.1103/physrevresearch.4.043150

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Quantum batteries (QBs) exploit collective quantum resources to surpass the limits of classical energy storage and power delivery. We analyze N -qubit cavity-coupled QBs governed by Dicke and Tavis-Cummings models under Gaussian driving and open-system dynamics. Finite-size scaling laws O ( N ) ∼ N α demonstrate an optimal region of relaxation and dephasing where coherent driving stabilizes entanglement entropy growth for thermodynamic observables (maximum energy E max , charging time τ , and maximum power P ¯ max ) and for qubit and cavity entanglement entropies. The Dicke model exhibits entropy-suppressed extensive behavior, while the Tavis-Cummings model achieves superextensive scaling with α E max ∈ [ 1.08 , 1.26 ] , α τ ≈ − 0.49 , and α P ¯ max ∈ [ 1.57 , 1.73 ] , supported by qubit-cavity entanglement. We demonstrate that dissipation can act as a stabilizer source, yielding scaling benchmarks that are relevant to several experimental platforms. Our findings connect entanglement, dissipation-enhanced scaling laws, and superabsorption, outlining a pathway toward scalable quantum batteries offering practical quantum advantage.
Quantum batteries have emerged as a platform for investigating whether quantum effects can accelerate energy storage beyond classical limits. Although a variety of charging schemes have reported signatures of quantum advantage, the fundamental physical requirements for achieving superextensive charging power remain insufficiently understood. Here, we show that, in addition to Hamiltonian locality, a key structural property, g-extensiveness, quantifying the distribution of interaction energy across lattice sites places a fundamental bound on charging performance in spin-lattice models. We prove that superextensive power scaling is possible only when the interaction-energy distribution becomes increasingly nonuniform, with the maximal local weight growing with system size. This criterion explains why many previously studied protocols fail to exhibit superextensive power, even when the Hamiltonians involve large participation numbers. We further demonstrate that this condition is realized in an experimentally relevant interacting model, where, despite fixed interaction order, the charging power scales superextensively. Our results establish g-extensiveness as a necessary resource for quantum advantage in direct-charging protocols and provide a systematic framework for identifying and engineering physically feasible quantum batteries capable of outperforming classical counterparts in charging power.
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.
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