Asymptotic freedom in the dephased charging of quantum batteries

Abstract

Quantum batteries, small-scale energy storage devices based on quantum systems, offer the potential for enhanced charging performance through quantum effects such as coherence and collectivity. In this work, we study the collective charging of quantum batteries consisting of N qubits, coupled to a driven qubit charger in a star configuration, with controlled pure dephasing acting on the charger. We investigate how an "asymptotic freedom"-like behavior, in which all the energy deposited into the battery can be extracted as work, resulting in the ergotropy-to-energy ratio approaching unity, can emerge in the steady state of the battery. We show that the ergotropy-to-energy ratio increases with the number of qubits and approaches unity asymptotically as 1 - O(1/N). In the large-N limit, the emergence of approximate ground-state degeneracy of the collective battery system leads to this asymptotic freedom behavior, despite the battery state remaining mixed. We also discuss the scaling behavior of the charging time of the battery with N.

Figures (9)

• Figure 1: Schematic diagram of a quantum battery $\mathrm{B}$ consisting of $N$ independent identical systems, coupled to a quantum charger $\mathrm{C}$ driven with strength $F$, where the charger is also subject to dephasing at a rate $\gamma_{\mathrm{C}}$.
• Figure 2: Variation of the total energy $E_{\mathrm{B}}$ and ergotropy $\mathcal{E}_{\mathrm{B}}$ of the battery in the steady state under intermediate driving ($F/g = 0.5$) as a function of the number of qubits $N$. The other parameters are $\omega_{\mathrm{B}} = \omega_{\mathrm{C}} = \omega_{\mathrm{d}} = 1$ and $g = 1.0\,\omega_{\mathrm{B}}$.
• Figure 3: Variation of steady-state ergotropy relative to the total energy ($\mathcal{E}_{\mathrm{B}}/E_{\mathrm{B}}$) as a function of the number of qubits ($N$) for (a) strong driving $F = 10 \omega_{\mathrm{B}}$$(F/g = 10)$, (b) intermediate driving $F = 0.5 \omega_{\mathrm{B}}$$(F/g = 0.5)$, and (c) weak driving $F = 0.2 \omega_{\mathrm{B}}$$(F/g = 0.2)$. The other parameters are the same as in Fig. \ref{['fig:energy and ergotropy for F = 0.5']}. The ratio $\mathcal{E}_{\mathrm{B}}/E_{\mathrm{B}}$ is given by $\mathcal{E}_{\mathrm{B}}/E_{\mathrm{B}} = 1-2\delta(N) N^{-1}$, where $\delta(N)$ is the population of the excited states of the passive state at a given $N$ (see Appendix \ref{['app:A']} for a detailed derivation of this relation).
• Figure 4: For a battery of $N = 8$ qubits under strong driving ($F/g = 10$): (a) Absolute values of the steady-state density matrix elements of the battery in the symmetric Dicke basis. (b) Populations fitted to the trial function given by Eq. \ref{['eq:pnsd']} using the optimal parameters $\alpha = 0.00104$, $\beta = 0.0107$, $\mu = -0.637$, and $\zeta = 0.0345$. With these optimal parameters, the fidelity value of the trial state given by Eq. \ref{['eq:pnsd']} is 0.9.
• Figure 5: For $N = 8$ qubits in the battery under intermediate driving ($F/g = 0.5$) (a) Absolute values of the steady-state density matrix elements of the battery in the symmetric Dicke basis. This state can be well approximated by the trial state given by Eqs. \ref{['eq:rhoid']}--\ref{['eq:psi2']} with a fidelity of 0.923, using the optimal parameters $\xi_1 = 0.054 + 2.603\,i$ and $\xi_2 = 0.047 - 1.960\,i$. (b) Absolute values of the corresponding passive-state density matrix elements of the battery. The other parameters are the same as in Fig. \ref{['fig:energy and ergotropy for F = 0.5']}.