Quadratic power enhancement in extended Dicke quantum battery

TL;DR

This work introduces a two-mode extended Dicke quantum battery where one cavity mode is dispersive, enabling genuine quantum advantage through $N^2$ scaling of both quantum correlations and charging speed. The authors derive an effective Hamiltonian with two-axis-twist–like spin squeezing and show quadratic power scaling is achievable in experimentally realistic parameter regimes, while maintaining energy efficiency. They propose circuit QED implementations with parametric drives to realize the anisotropy and multimode coupling, and demonstrate robustness to dissipation, including scenarios where engineered dissipation stabilizes fast charging. Overall, the study provides a practical route to high-power, robust quantum batteries with tunable performance, merging theoretical scaling insights with feasible experimental platforms.

Abstract

We demonstrate a quadratic enhancement of power in a battery consisting of $N$ two-level systems or spins interacting with two photonic cavity modes, where one of the modes is in the dispersive regime. In contrast to Dicke batteries, the power enhancement arises from a $N^2$ scaling of both quantum correlations and speed of evolution, thus highlighting genuine quantum advantage. Moreover, this hybrid setup is experimentally realizable and ensures that power enhancement is not achieved at significant cost to energy efficiency, while allowing for greater tunability and stable operation in the presence of noise.

Figures (5)

• Figure 1: Two mode Dicke quantum battery. (a) Schematic of the quantum battery model containing two cavity modes (red and orange) and the spin ensemble is spatially placed inside the cavity such that it is coupled with both the modes. (b) Whispering-gallery-mode resonator Minev2013, consisting two superconducting ring resonator (black), one placed on each layer (blue), which are seperated by a thin vacuum gap. The qubits are carved directly on the resonator of one layer (red) and out-of-plane fields (green) couple the two layers. (c) Circuit-QED representation of the model. The resonator in red box represents cavity mode $\hat{c}$ and the one in orange box is mode $\hat{b}$, which is parametrically driven through a flux-pumped superconducting quantum interference device (SQUID) Yamamoto2008 to get the required anisotropy in mode $b$. The two resonators are coupled to transmon qubits (in blue box) via coupling capacitors $C_{c}$ and $C_{b}$, respectively.
• Figure 2: Dynamics of two-mode QB. (a) Maximum charging energy per spin as a function of number of spins $N$ in the ensemble for $\tilde{\Delta}_s=\Delta_c = 0.7~\omega_c$, $\Delta_b= 101~\omega_c$, $g_c=0.05~\omega_c$, $\delta_b=-1$, and $g_b = 0~\omega_c$ (blue triangles) and $g_b=0.9~\omega_c$ (red circles). (b) Maximum charging power as a function of $N$ for same parameters, with short and long dashed lines representing the upper bound on charging power JuliaFarre2020, for $g_b/\omega_c = 0, 0.9$, respectively. (c) and (d) Average battery variance ${\langle \Delta \hat{H}_B^2 \rangle}_\tau$ and Fisher information ${\langle I_E \rangle}_\tau$, respectively, computed at time $\tau$ where power is maximum. Legends in (b)-(d) show the scaling of the quantities with $N$ obtained from best fit curve, with the lines joining the markers being the best fit lines. Black dotted lines in (a-d) represents parallel charging case, where each spin is charged individually.
• Figure 3: Scaling of bounds in the two-mode quantum battery. (a) Scaling of power (or extensivity) of the QB as a function of relative strength of spin-spin interaction $\chi_{b}$. Different curves corresponds to different $\tilde{\Delta}_s = \Delta_c$ for $\delta_b=-1$, equally distributed between ${\Delta}_c/\omega_c = 0.2$ and $1$. Strength of spin-spin interaction is controlled using $g_b/\omega_c$, which varies from $0.2$ to $2$, with $g_b/\omega_c = 0.9$ marked by vertical dashed line. (b) Same as (a) but for $\Delta_c/\omega_c=1.0$ and different anisotropy $\delta_b$, equally distributed between $-1$ and $1$. (c)-(d) Scaling of $P_{\text{sat}}$ (or bound saturation) as a function of spin-spin interaction strength, for same parameters as in (a) and (b), respectively. Other simulation parameters are $\Delta_b = 101~\omega_c$ and $g_c = 0.05 \omega_c$ and $\alpha_{r_b}$ is estimated using data from $N = 75$ to $100$ spins. Dot-dashed red curve in (a) and (c) marks the minimum enhancement achievable in the two mode case.
• Figure 4: Decoherence dynamics in the two mode quantum battery. Battery energy fluctuations ${\langle \hat{J}_z \rangle}-\overline{{\langle \hat{J}_z \rangle}}$ as a function of time for $\chi_b = 0.075~\omega_c$ with (solid) and without (dashed) decoherence. The dynamics was simulated for $N=10$, $\Delta_b=100$, $\delta_b\approx-1$, $g_c = 0.05$, $\kappa_{c/b} = 10^{-5}$ and $\gamma_{-1}=2\gamma_{0}=\gamma$ (in units of $\omega_c=1$). Vertical dotted lines marks the approximate time after which battery energy stabilizes.
• Figure 5: Dynamics in two mode quantum battery. Charging energy per spin as a function of charging time for the quantum battery with $N=100$ spins, $\Delta_c = \Delta_s = 1~\omega_c$, $\Delta_b = 101~\omega_c$, $g_c = 0.05~\omega_c$, $g_b = 2~\omega_c$ and $\delta_b=-1$. Solid lines correspond to the dynamics generated from full Hamiltonian $\hat{H}$ in Eq. \ref{['Eq:Hlab']} of the main text and dashed lines represent the effective dynamics generated from SW transformed Hamiltonian $\hat{H}_{sq}$ in Eq. \ref{['Eq:HamTAT']}. The inset zooms the region around first peak of energy.