Dissipative Quantum Battery in the Ultrastrong Coupling Regime Between Two Oscillators

Abstract

In this work, we propose an open quantum battery that stores and releases energy by employing a two-mode ultrastrongly coupled bosonic system, with one mode (the charger) coupled to an independent heat reservoir. Our results demonstrate that both the charging energy and ergotropy of the quantum batteries can be significantly enhanced within the ultra-strong coupling regime and across a broader temperature range in transient time. A unidirectional energy flow is achieved by controlling the system's initial state through its two-mode squeezed ground state. Furthermore, we show that the steady-state stored energy, along with its corresponding ergotropy, can be enhanced at larger temperatures and stronger coupling strengths. Notably, a purely beam-splitter or two-mode squeezing interaction yields zero ergotropy. These findings indicate that the enhanced stored energy and ergotropy of the quantum battery arises principally from the combined effects of beam-splitter and parametric amplification (squeezing) couplings. In addition, the presence of the squared electromagnetic vector potential term can prevent a phase transition and achieve a significant charging energy and high ergotropy in the deep-strong coupling regime. The results presented herein enhance our understanding of the operating principles of open bosonic quantum batteries.

Figures (12)

• Figure 1: Schematic representation of the bipartite quantum battery model. It consists of two oscillators with cavity mode $a$ (the charger) and matter $b$ mode (the battery) that are directly coupled to one another, and the mode $a$ is coupled to an independent reservoir. Here, we isolate the battery from the heat reservoir, but the charger is driven by a heat reservoir at temperature $T$.
• Figure 2: The behavior of the stored energy, $\Delta E_{b}$, and its corresponding ergotropy, $\mathcal{E}$ are presented as a function of time $t$ for various coupling strengths in panels (a) and (b), and different temperatures in panels (c) and (d) under resonant condition when considering the initial state $\rho(0)=|00 \rangle_{ab} \langle 00|$. In panels (c) and (d), the red solid, blue dashed, green dashed-dotted, and magenta dotted lines correspond to temperatures with $T_a/\omega_b=0.5, 1, 2, 5$. The following parameters are used: (a) and (b) $T_{a}=\omega_{b}$; (c) and (d) $g=0.3 \omega_b$. Other parameters are $\omega_{a}=\omega_{b}=\omega$, and $\gamma^{a}=10^{-3} \omega_{b}$. All parameters are expressed in units of the frequency $\omega_b$.
• Figure 3: The behavior of the stored energy $\Delta E_{b}$, and its corresponding ergotropy $\mathcal{E}$ are presented as a function of time $t$ for various coupling strengths in panels (a) and (b), and different temperatures in panels (c) and (d) under resonant condition considering the initial state $|G \rangle=|0 \rangle_{+} |0 \rangle_{-}$. The following parameters are used: (a) and (b) $T_{a}=\omega_{b}$; (c) and (d) $g=0.3 \omega_b$. Other parameters are $\omega_{a}=\omega_{b}=\omega$, and $\gamma^{a}=10^{-3} \omega_{b}$. All parameters are expressed in units of the frequency $\omega_b$.
• Figure 4: The squeezing parameters $r_{\pm}$ are plotted as a function of the coupling strength $g$. The parameter can take $\omega_{a}=\omega_{b}=\omega$.
• Figure 5: Behavior of the stored energy $\Delta E_{b}$ and corresponding ergotropy $\mathcal{E}$ as functions of the coupling strengths $g_{\mathrm{bs}}$ and $g_{\mathrm{sq}}$ (a, b), and temperature $T_a$ and coupling strength $g$ (c, d) under resonant condition. The parameters are set as $T_a=\omega_b$ for panels (a) and (b), $g_{\mathrm{bs}}=g_{\mathrm{sq}}=g=0.3 \omega_{b}$ for panels (c) and (d), and other parameters can take $\omega_{a}=\omega_{b}=\omega$, with all parameters expressed in units of the frequency $\omega_b$.