Connection-topology--dependent energy transport and ergotropy in quantum battery networks with reciprocal and nonreciprocal couplings

Abstract

The realization of scalable quantum battery architectures requires concern not only with how much energy can be stored, but also with how energy is transported, distributed, and converted into extractable work across connected battery nodes. While previous studies mainly focused on collective charging in multi-cell quantum batteries, the topology-dependent transport law and the corresponding work-oriented performance of quantum battery networks remain largely unexplored. In this work, we investigate quantum battery networks with engineered reciprocal and nonreciprocal couplings and compare different connection topologies, including cascaded and parallel architectures, within a unified transport framework. In the nonreciprocal regime, the optimal coupling follows distinct scaling laws for the two connection topologies, namely $J_{\rm op}^{c}\propto N$ for cascaded transport and $J_{\rm op}^{p}\propto N^{-1/2}$ for parallel charging in the large-$N$ limit. In reciprocal cascaded networks, a parity-dependent spectral response produces an odd-even transport effect that is absent in the nonreciprocal and parallel configurations. We further analyze the role of thermal and squeezed reservoirs and show that thermal noise mainly increases passive energy, whereas squeezing enhances ergotropy and thus the useful fraction of stored energy. These results shift the emphasis from charging enhancement to transport engineering and provide architecture-level design principles for quantum battery networks.

Figures (6)

• Figure 1: Multi-body quantum batteries in the cascaded (a) and parallel (b) configurations, consisting of a charger (C) and $N$ battery modes ($b_i$). Steady-state stored energy as a function of the battery number $N$ for cascaded (c) and parallel (d) schemes. Inset: optimal coupling strength $J_{\rm op}$ varies with $N$. The parameters used are $\kappa/\omega=0.003$, $\epsilon/\omega=0.01$, and $J=J_{\rm{op}}$.
• Figure 2: Energy distribution across the charger and battery modes for different coupling strengths $J/\omega=0.001$ (a, d), $J=J_{\rm op}$ (b, e), and $J/\omega=0.01$ (c, f). The cascaded configuration is shown in (a)–(c), while the parallel configuration is shown in (d)–(f). Dotted, dashed, and solid curves represent the stored energy in the charger, the first battery, and the second battery, while markers denote the analytical results. The other parameters are $\kappa/\omega=0.003$, $\epsilon/\omega=0.01$, and $N=2$.
• Figure 3: Steady-state stored energy as a function of the battery number $N$ under nonreciprocal coupling (NC) and reciprocal coupling (RC) for the cascaded (a) and parallel (b) configurations at $J=J_{\rm op}$. Panels (c)–(f) show the steady-state stored energy versus the coupling strength $J$: the cascaded configuration in (c, e) and the parallel configuration in (d, f), with $N=3$ for (c, d) and $N=4$ for (e, f). The other parameters are $\kappa/\omega=0.003$, $\epsilon/\omega=0.01$.
• Figure 4: Time evolution of the stored energy versus the scaled time for $N=3$ in (a, b), and $N=4$ in (c, d). The parameters are $\kappa/\omega=0.003$, $\epsilon/\omega=0.01$, and $J=J_{\rm op}$.
• Figure 5: Charging dynamics of Stored energy and ergotrop. Top row: single battery ($N=1$). Middle row: cascaded configuration with $N=2$. Bottom row: parallel configuration with $N=2$. The solid line, the dashed line, and the dotted line represent $n_{\rm th}=0$, $n_{\rm th}=1$, and $n_{\rm th}=2$, respectively. The other parameters are $\kappa/\omega=0.003$, $\epsilon/\omega=0.001$, and $J=J_{\rm op}$.