High-Power Collective Charging of a Solid-State Quantum Battery

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of $N$ two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model (“Dicke QB”), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode (“Rabi QB”). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like $\sqrt{N}$ for $N\gg 1$.

Figure 1

(a) An array of identical Rabi quantum batteries operating in parallel. The elementary building block (red box), consists of a two-level system with an energy separation $\hslash {\omega }_a$ between the ground $|g⟩$ and excited state $|e⟩$. Each two-level system is coupled to a separate photonic cavity (blue). The red arrow indicates a particle-hole transition induced by the photon field. (b) A Dicke quantum battery, where the same array of two-level systems is now embedded into a single cavity and interacting with a common photonic mode. (c) Charging, storage, and discharging protocol, as described in the text.

Figure 2

The dependence of the stored energy $E_{\overline{\lambda }}^{(♯)}({\tau }_c)$ (in units of $N\hslash {\omega }_c$) on ${\tau }_c$ (in units of $1/{\omega }_c$) for $\overline{\lambda }=0.5$ (green dashed line) and $\overline{\lambda }=2.0$ (blue solid line). (Inset) Same as in the main panel but for $\overline{\lambda }=0.05$ (red solid line). Results for the Tavis-Cummings model are denoted by a black dotted line. All shown data have been computed by setting $N=10$.

Figure 3

(a) The maximum stored energy $E_{\overline{\lambda }}^{(♯)}$ (in units of $N\hslash {\omega }_c$) as a function of $N$. Black squares denote results for the Tavis-Cummings model at $\overline{\lambda }=0.05$. Results for Dicke QBs refer to $\overline{\lambda }=0.05$ (red circles), $\overline{\lambda }=0.5$ (blue triangles), and $\overline{\lambda }=2.0$ (green diamonds). Dashed lines indicate the values relative to the parallel-charging case. (b) Same as in (a), but as a function of $\overline{\lambda }$ for $N=6$ (black squares), $N=8$ (red circles), $N=10$ (blue triangles), and $N=12$ (green diamonds). (c) The maximum charging power $P_{\overline{\lambda }}^{(♯)}$ (in units of $\overline{\lambda }N\sqrt{N}\hslash {\omega }_c^2$) as a function of $N$. Color coding and labeling is the same as in (a). The thin horizontal lines are best fits to the numerical results, indicating the asymptotic values of the maximum power at large $N$: ${\lim }_{N\gg 1}{P}_{\overline{\lambda }}^{(♯)}/(\overline{\lambda }N\sqrt{N}\hslash {\omega }_c^2)=0.586$ for $\overline{\lambda }=0.05$ (red), 0.858 for $\overline{\lambda }=0.5$ (blue), and 0.847 for $\overline{\lambda }=2$ (green). (d) Same as in (c), but as a function of $\overline{\lambda }$. Color coding and labeling as in (b).