Quantum advantage bounds for a multipartite Gaussian battery

Abstract

We demonstrate the possibility of a genuine quantum advantage in the efficiency of quantum batteries by analyzing a model that enables a consistent comparison between quantum and classical regimes. Our system consists of $N$ harmonic oscillator cells coupled to a common thermal reservoir, evolving through Gaussian states. We define the global efficiency as the ratio of extractable work (ergotropy) to stored energy, and derive analytical bounds that distinguish, in order of increasing efficiency, regimes characterized by classical squeezing, quantum squeezing without entanglement, and genuine entanglement. Moreover, numerical simulations support the emergence of a similar hierarchy for the thermodynamic efficiency, defined as the ratio between ergotropy and the total thermodynamic cost of the charging process.

Figures (4)

• Figure 1: (a) Plot of $E_{\mathrm{B}}(t)$ (units $\hbar\omega_0$) as a function of $t/\tau$ for $N=6$ (blue), $N=12$ (green) and $N=18$ (red). For $N=6$, density plots of $\eta_{\mathrm{glob}}=\eta_{\mathrm{glob}}(t^*)$ (b) and $\eta_{\mathrm{th}}=\eta_{\mathrm{th}}(t^*)$ (c), as a function of $T$ and $T_0$ (units $\hbar\omega_0/k_{\mathrm{B}}$). The dashed line in panels (b) and (c) represents the boundary $T=T^{*}$. Here $\alpha_l=1$, $\gamma_0=5\,\omega_0$ and $\omega_D=2\,\omega_0$.
• Figure 2: Density plot of $r=r(t^*)$ as a function of $T$ and $T_0$ (units $\hbar\omega_0/k_{\mathrm{B}}$). The yellow line corresponds to $\lambda_-(t^*)=1/2$. Here $N\!=\!4$, $\alpha_l\!=\!1$, $\gamma_0\!=\!5\,\omega_0$, $\omega_D=2\,\omega_0$.
• Figure 3: Density plot of $\eta_{\mathrm{glob}}=\eta_{\mathrm{glob}}(t^*)$ as a function of $T$ and $T_0$ (units $\hbar\omega_0/k_{\mathrm{B}}$) with $N=6$ and (a) $\gamma_0=0.99\,\omega_0$, $\omega_D=12.5\,\omega_0$; (b) $\gamma_0=1.63\,\omega_0$, $\omega_D=3.49\,\omega_0$. In both panels, the white dot indicates the common operating point chosen for the comparison, while the yellow line denotes the boundary between classical and quantum squeezing, defined by the condition $\lambda_-(t^*)=1/2$. In (a), the operating point lies in the classical squeezing region, while in (b) it falls within the quantum squeezing regime. (c) Table summarizing the precise values of the model parameters and relevant physical quantities corresponding to the operating point in both scenarios.
• Figure 4: Density plot of $\mathcal{N}=\mathcal{N}(t^*)$ as a function of $T$ and $T_0$ (units $\hbar\omega_0/k_{\mathrm{B}})$. The white line, $\nu_-^{(\mathrm{PT})}(t^*)=1/2$, marks the boundary between entangled and separable states. The yellow line, $\lambda_-(t^*)=1/2$, separates the regions of quantum and classical squeezing (see Fig. \ref{['fig:Fig3']}). Here, $N=4$, with a balanced partition $N_{\mathrm{A}}\!=\!N_{\mathrm{B}}\!=\!2$, $\alpha_l=1$, $\gamma_0=5\,\omega_0$ and $\omega_{\mathrm{D}}=2\,\omega_0$.