Superextensive charging speeds in a correlated quantum charger

TL;DR

The paper investigates whether interactions in a Floquet-driven quantum charger can boost energy transfer between two periodic drives beyond noninteracting limits. Using a long-range spin-chain model (all-to-all and power-law couplings) in a Floquet framework, it introduces a work operator whose spectrum determines optimal energy transfer and demonstrates superlinear charging $W \propto N^{1+\delta}$ up to a crossover size $N^*$, with a high-frequency mechanism explained by a van Vleck expansion. It shows that both high-frequency eigenstates and spin-coherent states can approximate the Floquet optimum and exhibit superlinear scaling, and it presents an echo protocol to stabilize the desired work states in the steady state. The results illuminate how cooperative many-body dynamics enable enhanced energy conversion, offer concrete experimental paths (e.g., trapped ions), and suggest strategies for scalable implementation and extension to dissipation and broader models.

Abstract

We define a quantum charger as an interacting quantum system that transfers energy between two drives. The key figure of merit characterizing a charger is its charging power. Remarkably, the presence of long-range interactions within the charger can induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units. Using the driven Lipkin-Meshkov-Glick model and power-law interacting spin chains, we show that this effect persists up to a critical system size set by the breakdown of the high-frequency regime. We discuss optimal work output as well as experimentally accessible initial states. The superlinear charging effect can be probed in trapped-ion experiments, and positions interacting Floquet systems as promising platforms for enhanced energy conversion.

Figures (7)

• Figure 1: Energy flow between drives with frequencies $\omega_1$ and $\omega_2$ through a many-body quantum charger. (a) Parallel, noninteracting charger. (b) Collective, interacting charger. (c) Work per spin in a Floquet steady state. Long-range interactions enhance the charger's performance superlinearly in the system size $N$.
• Figure 2: Superlinear work scaling with $N$ of an interacting quantum charger. (a) Maximum work over a period scales quadratically in $N$ in the presence of interactions (dots), crossing over to linear scaling at large $N$. The noninteracting charger (solid) always scales linearly. (b) Same as (a) depending on the rescaled couplings. (c) Work of optimal Floquet state also scales superlinearly for intermediate $N$. (d) Superlinear steady-state energy flow via dynamics of Floquet states (evaluated at multiples of the period). Parameters: $\omega_1=2\pi$, $\omega_2=\pi$, $\phi_1=0$, $\phi_2=\pi/4$, $\mathbf{h}_1=0.1\hat{\mathbf{y}}+\hat{\mathbf{z}}$$\mathbf{h}_2=\hat{\mathbf{x}}+0.1\hat{\mathbf{y}}$, (a),(c) $J=-0.05$, $\mathbf{h}_0=0.01\hat{\mathbf{x}}$ (d) $J=-0.02$, $\mathbf{h}_0=0.25\hat{\mathbf{x}}$.
• Figure 3: (a) Maximum work, and (b) work of optimal Floquet state, for drive 1 over a period as a function of system size for various power-law interactions with range $\gamma$. Parameters: $J=1$, $T=0.1$, $\mathbf{h}_0=0$, $\mathbf{h}_1=0.86\mathbf{\hat{x}}+0.25\mathbf{\hat{y}}+0.41\mathbf{\hat{z}}$, $\mathbf{h}_2=0.18\mathbf{\hat{x}}+0.67\mathbf{\hat{y}}+0.72\mathbf{\hat{z}}$, $\phi_1=0$, $\phi_2=\pi/2$.
• Figure 4: Maximum work of Floquet states in the high-frequency regime. (a) $\omega_1=\omega_2$. Analytical expression in Eq. \ref{['eq:high freq analytical']} (dashed) captures data for small $JN\ll \omega$. (b) Same as in (a) but for different amplitudes $h/\omega$, see legend. (c) Various frequency ratios $p/q=\omega_1/\omega_2$ as indicated. We collapse the data according to Eq. \ref{['eq:work freq scaling']}. Parameters: (a) $J=1$, (b) $J=1$, $T=0.1$, (c) $J=0.1$. Other parameters as in Fig. \ref{['fig:long_range']}.
• Figure 5: Work for high-frequency and coherent states approximations of Floquet states (experimentally preparable). (a) High-frequency regime ($\omega_1=\omega_2$): Superlinear steady-state pumping is observable both by the high-frequency approximation (dotted) and by the spin-coherent state approximation (dashed) of the optimal Floquet state (solid). (b), (c) Average work per cycle and per spin for different frequency ratios $\omega_1/\omega_2=p/q$ as indicated (top panels). Bottom panels: Total polarization per spin in the Floquet state. Parameters as in Fig. \ref{['fig:long_range']}.