Sunburst quantum Ising battery under periodic delta-kick charging

TL;DR

The paper investigates a sunburst quantum Ising battery driven by periodic delta-kicks to evaluate energy storage, work extraction, and charging power in both chaotic and integrable regimes. By analyzing the Floquet spectrum with random-matrix theory, it demonstrates a transition to quantum chaos and identifies a finite window ($n_b\leq 4$) where chaotic dynamics yield a superlinear charging-power scaling accompanied by stable energy storage, while the integrable regime permits optimal storage/extraction irrespective of the charger’s initial state. Analytical results in the near-integrable limit provide explicit expressions for stored energy $E(n)=\delta|(F_n)_{21}|^2$ and ergotropy, with $E_{\max}=\delta$ and optimal extraction at $|(F_n)_{21}|^2=1$, and show that under certain kick parameters entanglement is unnecessary. Quantum Fisher information analyses show no multipartite entanglement among battery qubits, indicating that the observed quantum advantage is classical in origin, in contrast to many integrable QB models. Overall, the work presents a short-range, periodically driven quantum battery that simultaneously achieves optimal storage, stable storage, and charging-power advantage, enriching the design space for robust quantum energy devices.

Abstract

Most quantum batteries studied so far with notable exception of Sachdev-Ye-Kitaev (SYK) batteries are based on integrable models, where superlinear scaling of charging power and hence a quantum advantage can be achieved, but at the cost of unstable stored energy due to integrability. Here, by considering the sunburst quantum Ising battery driven by periodic delta-kicks, we show that in the quantum chaotic regime a quantum advantage is achieved for number of batteries $n_b\leq 4$, together with excellent stability of energy storage. In the integrable regime optimal energy storage and extraction are possible irrespective of the initial state of the charger. Finally, we show that the observed advantage does not originate from multipartite entanglement within the battery subsystem and is therefore classical in nature.

Figures (5)

• Figure 1: (Left) The variation of $\langle \tilde{r} \rangle$ with $h$ is plotted by keeping $J=\delta = \kappa=1$ for three different number of batteries, $n_b=2,3,4$. A clear transition from integrability for $h= 0$ to quantum chaotic nature for $h\approx 1$ is captured through average ratio of spacing. Two solid gray lines correspond to $\langle \tilde{r}\rangle \approx 0.386$ and $\langle \tilde{r}\rangle \approx 0.53$. (Right) Same is plotted with $\kappa$ by keeping $J=\delta = h=1$ for three different number of batteries, $n_b=2,3,4$. The expected transition from integrability to chaos with increasing $\kappa$ is clearly seen. The pronounced dip at $\kappa=2$ is due to $U_{cb}$ becoming a local operator (Eq. \ref{['eq:U_specialcase']}) which maps a direct product state to another direct product state.
• Figure 2: The dynamics for $E$(green), $\xi$ and $S_L$ are plotted for the system size $L=6$, $n_b=1$ by keeping the parameters $J,\delta=1$, $\kappa=6$, $\tau= \pi/20$ and $h=0.1$. The symbols stand for the numerical results and the solid lines are to show the analytical results derived in Eqs. \ref{['eq:stored_eng_expression']}, \ref{['eq:ergotropy_expression']} and \ref{['eq:entropy_expression']}. The horizontal cyan line correspond to maximum possible stored energy, $\delta$.
• Figure 3: The dynamics of $\frac{E(n)}{n_b}$ is shown for $n_b=4$(dark yellow), $5$(blue) and $6$(red). The total system sizes are chosen as $L+n_b=13$ and the parameters are chosen as $J,h,\kappa,\delta=1$ and $\tau=\pi/4$.
• Figure 4: The charging time is plotted against $n_b$ in the left column for fixed charger length $L=6$. The top-left curve corresponds to $\tau=\pi/4$ while the bottom-left correspond to $\tau=\pi/4+0.1$. The right column corresponds to scenario in which the total length of charger and battery is kept constant, 13 to be precise. Like in the left column case, top plot correspond to $\tau=\pi/4$ while bottom plot corresponds $\tau=\pi/4+0.1$. Other parameters are chosen as $J,h,\kappa,\delta=1$.
• Figure 5: Power from Eq: \ref{['eq:power_defn']} (on the left $y$-axis)and the corresponding bound from Eq: \ref{['eq:bound_power']} (on the right $y$-axis) have been plotted at the charging time ($m\tau$) with the $n_b$. A non-linear increase in power with increasing number of batteries is a clear signature of advantage over parallel classical charging scheme.