Cavity-Heisenberg spin-$j$ chain quantum battery and reinforcement learning optimization

TL;DR

This work introduces a cavity-Heisenberg spin-chain quantum battery with spin-$j$ particles and analyzes charging under both closed and open dynamics, incorporating spin-spin interactions, temperature, and cavity dissipation. A soft actor-critic reinforcement learning framework optimizes the time-dependent cavity–battery coupling $g(t)$ to maximize stored energy and charging power, revealing a regime where larger spin sizes yield higher energy storage and power. In closed systems, increased cavity–spin entanglement $E_\mathcal{N}$ correlates with higher energy, while in open systems the energy benefits correlate with reduced entanglement, highlighting distinct mechanism differences due to dissipation. The results demonstrate the potential of RL-based control to enhance QB performance and provide design insights for robust energy storage in realistic quantum devices.

Abstract

Machine learning offers a promising methodology to tackle complex challenges in quantum physics. In the realm of quantum batteries (QBs), model construction and performance optimization are central tasks. Here, we propose a cavity-Heisenberg spin chain quantum battery (QB) model with spin-$j (j=1/2,1,3/2)$ and investigate the charging performance under both closed and open quantum cases, considering spin-spin interactions, ambient temperature, and cavity dissipation. It is shown that the charging energy and power of QB are significantly improved with the spin size. By employing a reinforcement learning algorithm to modulate the cavity-battery coupling, we further optimize the QB performance, enabling the stored energy to approach, even exceed its upper bound in the absence of spin-spin interaction. We analyze the optimization mechanism and find an intrinsic relationship between cavity-spin entanglement and charging performance: increased entanglement enhances the charging energy in closed systems, whereas the opposite effect occurs in open systems. Our results provide a possible scheme for design and optimization of QBs.

Figures (13)

• Figure 1: Schematic diagram of an RL algorithm for optimising the charging performance of a cavity-Heisenberg spin chain QB. An RL agent determines the external control action of the cavity-spin coupling $g(t)$ by observing the current state of stored energy $E(t)$ and average charging power $P(t)$ of the QB, thereby maximizing the stored energy and achieving a relatively high power. The optimization process consists of numerous iterations between the RL algorithm and the QB. Through this cycle, QB charging efficiency is refined to its optimal level.
• Figure 2: The dependence of (a)-(c) the stored energy $E(t)$ (in units of $\hbar\omega_{a}$), (d)-(f) average charging power $P(t)$ (in units of $\hbar\omega^{2}_{a}$), and (g)-(i) logarithmic negativity $E_\mathcal{N}(t)$ of closed system QB as a function of $\omega_a t$ for different values of spin $j$. The different curves in these plots stand for various spin-spin interaction $J$, as indicated in the legends. The cavity-spin coupling is chosen as $g = 1$.
• Figure 3: The contour plots of closed system QB's (a)-(c) stored energy $E(t_{P_{max}})$ (in units of $\hbar\omega_{a}$), (d)-(f) maximum charging power $P_{max}$ (in units of $\hbar\omega_{a}^{2}$), and the logarithmic negativity $E_\mathcal{N}(t_{P_{max}})$ as functions of the cavity-spin coupling strength $g$ and spin-spin interaction strength $J$ for different spin $j$: (a), (d) and (g) spin-$1/2$, (b), (e) and (h) spin-$1$, (c), (f) and (i) spin-$3/2$.
• Figure 4: Optimized results: (a)-(c) The dependence of the stored energy $E(t)$ (in units of $\hbar\omega_{a}$), (d)-(f) average charging power $P(t)$ (in units of $\hbar\omega^{2}_{a}$), and (g)-(i) logarithmic negativity $E_\mathcal{N}(t)$ of closed system QB as a function of $\omega_a t$ for different spin $j$.
• Figure 5: The time evolution of stored energy in pre-optimization and optimization for spin-$3/2$ under different interaction (a) $J=-1$, (b) $J=0$, and (c) $J=1$.