Enhanced Nonreciprocal Quantum Battery Performance via Nonlinear Two-Photon Driving

TL;DR

This work investigates enhancing QB performance by combining nonreciprocal energy transfer with nonlinear two-photon driving. It develops a two-mode QB model (charger and battery) driven by a quadratic drive and coupled to a shared environment, described by a Markovian Lindblad master equation with nonreciprocity implemented via $J = -i\mu(\Gamma/2)$ and a stability threshold $\epsilon < \Lambda/4$. The authors derive analytical steady-state expressions and show that increasing the drive strength $\epsilon$ boosts stored energy and ergotropy while larger local dissipation $\kappa$ diminishes steady-state values, and that symmetric versus asymmetric dissipation can be engineered to optimize performance. Compared to single-photon driving, nonlinear two-photon driving generally improves energy storage and ergotropy, with asymmetry tuning offering further gains; the proposal is experimentally feasible in optomechanical, superconducting, and magnonic platforms, making it a practical route toward efficient quantum energy transfer.

Abstract

Quantum batteries have attracted significant attention as efficient quantum energy storage devices.In this work, we propose a nonlinear two-photon driving quantum battery model featuring nonreciprocal dynamics that enables a highly efficient unidirectional charging mechanism through environmental engineering. Using a Markovian master-equation approach, we derive analytical solutions for the system dynamics and identify the parameter regime required for dynamical equilibration. Our results reveal that increasing the driving strength enhances both energy conversion and storage efficiency, albeit at the cost of longer equilibration times. Compared with single-photon driving, the two-photon process exhibits a pronounced advantage in energy capacity and entropy regulation, which becomes more prominent under stronger driving. Under asymmetric dissipation, optimizing the system-bath coupling can further improve performance. The proposed model is experimentally feasible and can be implemented across multiple quantum platforms, including photonic systems, superconducting circuits, and magnonic devices.

Figures (6)

• Figure 1: Illustration of two-photon driving quantum battery system: The charger is subject to a parametric drive (indicated by the red arrow), characterized by amplitude $\epsilon$, phase $\theta$, and frequency $2\omega_p$. The charger $a$ and the battery $b$ are directly coupled via a coherent Hamiltonian $\hat{H}_{\text{coh}}$. In addition, both modes are connected to a common dissipative environment, with decay rates $\Gamma_a$ and $\Gamma_b$, respectively. By tuning the relative strengths of the coherent and dissipative interactions, one can effectively break the system's reciprocity. The local damping rates are denoted by $\kappa_a$ and $\kappa_b$, corresponding to the charger and the battery, respectively.
• Figure 2: Figs (a)-(c) illustrate the dynamics of the QB's stored energy $E_b(t)/\omega$, ergotropy $\varepsilon(t)/\omega$, and the instantaneous power of the ergotropy $P_{\varepsilon b}$ as functions of the scaled time $Jt$, under varying local damping strengths $\kappa$. In this case, the driving amplitude is fixed at $\epsilon = 0.05\omega$. Figs (d)-(f) further explore how these three quantities evolve when the damping is fixed at $\kappa = 0.06\omega$ and the driving strength varies as $\epsilon/\omega = 0.03,\ 0.06,\ 0.09,\ 0.12$. In all panels, the horizontal axis represents the scaled time $Jt$. Other parameters are set as: $\kappa = \kappa_a = \kappa_b$, $\Gamma = \Gamma_a = \Gamma_b$, and $|J| = \Gamma/2 = 0.25\omega$.
• Figure 3: Figs (a) and (b) illustrate the functions of time $Jt$ evolution of the energy utilization ratio $\eta_{\varepsilon b/Eb}$ and the energy conversion ratio $\eta_{\varepsilon b/Ea}$ under various dissipation strengths $\kappa$. Figs (c) and (d) show how these ratios change with time under various driving strengths, with $\kappa$ held constant. In all panels, the horizontal axis denotes the rescaled time $Jt$. Other parameters are set as: $\kappa = \kappa_a = \kappa_b$, $\Gamma = \Gamma_a = \Gamma_b$, and $|J| = \Gamma/2 = 0.25\omega$.
• Figure 4: Figs (a) and (c) illustrate the dynamic evolution of the QB’s the relative storage ratio $\eta_{E_{b}/E_{b1}}$ and the relative ergotropy ratio $\eta_{\varepsilon_{b}/E_{b1}}$ under different $\kappa$ conditions, as a function of the characteristic scaling time $Jt$. Here, $\epsilon = 0.05 \omega$. Figures (b) and (d) explore the time evolution of these two quantities further, under a fixed dissipation strength of $\kappa = 0.06 \omega$, while varying the driving strength parameters $\epsilon/\omega = 0.03, 0.06, 0.09, 0.12$. Other parameters include: $\kappa = \kappa_{a} = \kappa_{b}$, $\Gamma = \Gamma_{a} = \Gamma_{b}$, $|J| = \Gamma /2$, and $|J| = 0.25 \omega$.
• Figure 5: Figs (a) and (b) display the evolution of the efficiency ratio $\chi(t)$ between a nonlinear two-photon driving QB and a single-photon QB under different conditions. Fig. (a) illustrates the relationship as a function of the dissipation rate $\kappa$, while Fig. (b) shows its dependence on the driving field strength $\epsilon$. The other parameters are set as follows: $\kappa = \kappa_a = \kappa_b$, $\Gamma = \Gamma_a = \Gamma_b$, $|J| = \Gamma / 2$, and $|J| = 0.25\omega$.