Asymptotic freedom in the dephased charging of quantum batteries

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 a 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.