Entanglement and Dynamical Scaling Laws in Quantum Superabsorption

TL;DR

This paper investigates how entanglement and dissipation influence the scaling laws of quantum batteries modeled by Dicke and Tavis--Cummings models, revealing conditions for optimal energy storage and power with potential experimental relevance.

Contribution

It introduces finite-size scaling laws for quantum batteries under Gaussian driving and open-system dynamics, highlighting the role of entanglement and dissipation in enhancing scalability and performance.

Findings

Tavis--Cummings model achieves super-extensive scaling of maximum energy and power.

Dissipation can stabilize entanglement growth and improve scaling.

Entanglement entropy growth is optimized in specific relaxation and dephasing regimes.

Abstract

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 $\mathcal{O}(N)\!\sim\!N^{\alpha}$ demonstrate an optimal region of relaxation and dephasing where coherent driving stabilizes entanglement entropy growth for thermodynamic observables (maximum energy $E_{\mathrm{max}}$, charging time $\tau$, and maximum power $\bar{P}_{\mathrm{max}}$) and for qubit and cavity entanglement entropies. The Dicke model exhibits entropy-suppressed extensive behavior, while the Tavis--Cummings model achieves super-extensive scaling with $\alpha_{E_{\mathrm{max}}}\!\in\![1.08,1.26]$, $\alpha_{\tau}\!\approx\!-0.49$, $\alpha_{\bar{P}_{\mathrm{max}}}\!\in\![1.57,1.73]$, 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 towards scalable quantum batteries offering practical quantum advantage.