Stabilizing ergotropy in Spin-Chain Quantum Batteries via Energy-Invariant Catalysis under Strong Non-Markovian Coupling

TL;DR

The paper addresses stabilizing the maximum extractable work, or ergotropy, in a spin-chain quantum battery (QB) strongly coupled to a structured cavity reservoir under non-Markovian dynamics, by introducing an energy-invariant catalyst. The system is modeled with a Nakajima–Zwanzig-type master equation incorporating a Gaussian memory kernel $\Gamma(t,s)= \kappa_1 \exp[-\kappa_2 (t-s)^2]$, and includes a spin chain with local energy $\omega_a$, exchange $J$, a single-mode cavity of frequency $\omega_c$, and a catalyst with energy $\omega_{\text{cat}}$ coupled via $\lambda$, plus cavity-spin coupling $g$. The ergotropy dynamics are computed from the evolving density matrix under these interactions, with initial conditions of a fully charged spin chain, vacuum cavity, and ground-state catalyst, and the key quantity $\mathcal{W}(t)$ is evaluated relative to the passive state. The main result is that increasing the catalyst-spin coupling $\lambda$ (and related spectral hybridization), tuning $\omega_c$, increasing the number of spins $N$, and adjusting $\omega_a$ can suppress ergotropy oscillations and promote a quasi-stationary work output; however, overly strong catalysis under strong system–environment coupling can destabilize extraction. This work demonstrates that energy-invariant catalysis is a viable control mechanism for robust QB performance in non-Markovian settings, with potential implications for superconducting circuits and trapped-ion platforms.

Abstract

Quantum batteries (QBs) have emerged as promising platforms for microscale energy storage, yet most existing studies assume weak system-environment coupling and Markovian dynamics. Here we explore how physical catalysis can regulate the maximum extractable work (ergotropy) of a spin-chain QB strongly coupled to a cavity environment. We model the system using a Nakajima-Zwanzig-type non-Markovian master equation and simulate the time evolution of ergotropy under various physical parameters. Our results show that increasing the catalyst-spin coupling, spin energy or cavity frequency can effectively suppress ergotropy oscillations and yield quasi-stationary ergotropy regime, while overly strong catalyst, especially when accompanied by increasing system-environment coupling under such conditions, can destabilize work extraction. This study demonstrates how quantum catalysis can serve as a control knob for optimizing battery performance in strongly coupled non-Markovian regimes.

Figures (5)

• Figure 1: (Color online) Schematics of a spin-chain quantum battery(QB) coupled to a cavity environment under the influence of a physical catalyst. The QB strongly interacting ($g$) with a structured cavity reservoir, consists of a chain of spin units $S_i$ coupled via exchange interaction $J$. A qubit-based catalyst, whose energy remains nearly constant during the evolution, is coupled to each spin via $\lambda$ .
• Figure 2: (Color online) a(i)$_{(i=1\sim4)}$ Ergotropy dynamics for the catalyst-free battery-cavity system. b(i)$_{(i=1\sim4)}$ Ergotropy (solid line) and catalyst energy (dashed line) dynamics for the full battery-catalyst-cavity system at increasing single-mode cavity field frequency $\omega_c$. Simulation parameters are $\omega_a$=0.25, $\kappa_1$=1.2, $\kappa_2$=0.8, $\omega_{cat}$=0.05, $g$=$J$=$\lambda$=0.01.
• Figure 3: (Color online) c(1)-c(4) Ergotropy dynamics for the catalyst-free battery-cavity system. d(1)-d(4) Ergotropy (solid lines) and catalyst energy (dashed lines) dynamics for the full battery-catalyst-cavity system, at increasing values of the memory kernel prefactor $\kappa_{1}$. Simulation parameters are $\omega_a$=0.5, $\omega_c$=0.25, $\lambda$=0.25, $\kappa_2$=0.05, $\omega_{cat}$=0.05, $g$=$J$=$\lambda$=0.05.
• Figure 4: (Color online) e(i)$_{(i=1\sim4)}$ Ergotropy dynamics in the absence of catalysis, i.e., for the battery-cavity system alone, f(i)$_{(i=1\sim4)}$ Ergotropy (solid lines) and catalyst energy (dashed lines) dynamics for the full battery-catalyst-cavity setup at increasing the memory kernel width $\kappa_2$. Simulation parameters are $\kappa_1$=0.05, $\omega_a$=0.5, $\omega_c$=0.25, $\omega_{cat}$=0.05, $g$=$J$=0.01, $\lambda$=0.2.
• Figure 5: (Color online) (a) Ergotropy dynamics in the absence of catalysis, i.e., for the battery-cavity system alone with $g$=0.05, $J$=0.04. (b) Ergotropy (solid lines) and catalyst energy (dashed lines) dynamics for the full battery-catalyst-cavity setup at increasing the local spin excitation energy $\omega_a$ with $g$=$J$=0.01. Simulation parameters are $\omega_c$=0.25, $\omega_{cat}$=0.05, $\kappa_1$=1.2, $\kappa_2$=1.8, $\lambda$=0.01.