Entanglement, coherence, and charging process of quantum batteries

Quantum devices are systems that can explore quantum phenomena, such as entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as the main element in their high performance in powerful charging. In this paper, we explore quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two- and three-cell battery, our results suggest that entanglement is not the main resource in quantum batteries, where there is a nontrivial correlation-coherence tradeoff as a resource for the high efficiency of such quantum devices.

Figure 1

Schematic diagram of a two-cell QB, e.g., a two-spin system, being charged through the parallel and collective charging, respectively. Local fields act on the cells, and the cells interact with each other along a collective charging. In collective charging, the system can evolve through an entangled state (gray balls).

Figure 2

Time evolution for (a) ergotropy, (b) instantaneous charging power, (c) entanglement, and (d) coherence of the two-cell QB for different values of the anisotropy parameter $\mathrm{\Delta }$. The coupling regime between the qubits is $J=\mathrm{\Omega }$.

Figure 3

Graph for the quantities ${\mathcal{E}}_{\text{fin}}\left(\mathrm{\Delta }\right)$ (in units of ${\mathcal{E}}_{\text{max}}$), $\overline{\mathcal{P}}\left(\mathrm{\Delta }\right)$ (as a multiple of ${\mathcal{P}}_{\text{max}}^{\parallel }$), $\overline{\mathcal{Q}}\left(\mathrm{\Delta }\right)$, and $\overline{\mathcal{C}}\left(\mathrm{\Delta }\right)$ as a function of $\mathrm{\Delta }$. The coupling regime between the qubits is $J=\mathrm{\Omega }$.

Figure 4

Graphs for the quantities ${\mathcal{E}}_{\text{fin}}\left(\mathrm{\Delta }\right)$ (in units of ${\mathcal{E}}_{\text{max}}$), $\overline{\mathcal{P}}\left(\mathrm{\Delta }\right)$ (as a multiple of ${\mathcal{P}}_{\text{max}}^{\parallel }$), $\overline{\mathcal{Q}}\left(\mathrm{\Delta }\right)$, and $\overline{\mathcal{C}}\left(\mathrm{\Delta }\right)$ as a function of $\mathrm{\Delta }$ and $J/\mathrm{\Omega }$ (in log scale). The regime of values for $J$ varies from $J=0.1\mathrm{\Omega }$ $[{log}_{10}(J/\mathrm{\Omega })=-1]$ to $J=10\mathrm{\Omega }$ $[{log}_{10}(J/\mathrm{\Omega })=1]$ and $\mathrm{\Delta }\in \{-1,-0.5,0,0.5,1\}$.

Figure 5

Time evolution for (a) ergotropy, (b) instantaneous charging power, (c) average entanglement, and (d) coherence of the three-cell QB for different values of the anisotropy parameter $\mathrm{\Delta }$. The coupling regime between the qubits is $J=\mathrm{\Omega }$, and for the three-cell QB we find ${\mathcal{E}}_{\text{max}}=6\hslash \omega$ and ${\mathcal{P}}_{\text{max}}^{\parallel }={\mathcal{E}}_{\text{max}}\mathrm{\Omega }$.

Figure 6

(a) Instantaneous ergotropy and (b) coherence for the dissipative charging process of the two-cell QB driven by Eq. (B1) for different values of the dissipative charging process. The Hamiltonian parameters are $J=\mathrm{\Omega }$, $t_{\text{min}}=\pi /2\mathrm{\Omega }$, and $\mathrm{\Delta }=1$.