Entanglement and Thermodynamic Scaling Laws in Quantum Superabsorption

TL;DR

This work analyzes N-qubit quantum batteries coupled to a single cavity mode under Gaussian driving and Markovian dissipation, comparing Dicke and Tavis–Cummings models. By deriving finite-size scaling laws for energy, time, and power and linking them to bipartite qubit–cavity entanglement, it shows that dissipation can act as a constructive resource, with a dephasing-dominated window yielding superextensive scaling in the Tavis–Cummings model. Coherent driving stabilizes entanglement growth, maintaining favorable scaling without erasing the cooperative advantage. The results map to several experimental platforms, offering a pathway to scalable quantum batteries with practical quantum advantage in energy storage and power delivery.

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 $\mathcal{O}(N)\!\sim\!N^α$ 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 $τ$, 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 $α_{E_{\mathrm{max}}}\!\in\![1.08,1.26]$, $α_τ\!\approx\!-0.49$, $α_{\bar{P}_{\mathrm{max}}}\!\in\![1.57,1.73]$, 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.

Figures (16)

• Figure 1: Scheme of the cavity–driven QB and dissipation channels. (a) An ensemble of $N$ identical qubits, each with a transition frequency $\omega_q$, are (b) collectively coupled to a single cavity mode of frequency $\omega_c$ with a coupling strength $g$. (c) The battery is charged by a resonant Gaussian drive $\eta(t)$ that excites the cavity (see below). (d) The cavity mode loses photons through leakage at a rate $\kappa$. (e) Each qubit undergoes pure dephasing at rate $\gamma^z$, which randomizes the relative phases without exchanging energy; (f) qubit relaxation occurs at a rate $\gamma^-$, corresponding to spontaneous decay from the excited state to the ground state.
• Figure 2: Maximum stored energy $E_{\max}$ as a function of qubit number $N$ and coupling strength $g/\omega_q$; $\kappa/\omega_q = \gamma^z/\omega_q = \gamma^-/\omega_q=10^{-3}$. Results are shown for Dicke (left) and Tavis--Cummings (right) Hamiltonians in the undriven (top) and driven (bottom) setups. Color scales are row-normalized: for each setup (driven or undriven), we divide by the maximum $E_{\max}$ across both scenarios and for all $(N,g/\omega_q)$ conditions.
• Figure 3: Entanglement entropy $S_q$, as a function of qubit number $N$ and coupling strength $g/\omega_q$, with the same parameters as in Fig. \ref{['fig:energy-nodiss']}. The panels compare the Dicke (left) and Tavis--Cummings (right) Hamiltonians for the undriven (top) and driven (bottom) setups. The color scales are row-normalized as in Fig. \ref{['fig:energy-nodiss']}, but using the maximum value of $S_q$.
• Figure 4: Maximum stored energy $E_{\max}$ as a function of $\kappa$ and qubit number $N$; $g/\omega_q = 0.1$, $\gamma^z/\omega_q = \gamma^-/\omega_q=10^{-3}$. The color scale is row-normalized, as in Fig. \ref{['fig:energy-nodiss']}, using the maximum value of $E_{max}$. The $\kappa$ rates are varied over the discrete set of values $\{10^{-3},\,10^{-2},\,0.1,\,0.2,\,0.3,\,0.4,\,0.5,\,0.6,\,0.7,\,0.8,\,0.9,\,1.0\}$.
• Figure 5: Maximum entanglement entropy $S_q$ as a function of $\kappa$ and qubit number $N$, with same parameters and $\kappa$ values as in Fig. \ref{['fig:energy_cav']}. Results are shown for Dicke (left) and Tavis--Cummings (right) Hamiltonians under undriven (top) and driven (bottom) conditions. Color scale is row-normalized, as in Fig. \ref{['fig:energy-nodiss']}, using the maximum value of $S_q$.