Ergotropy Activation and Coherence in Dissipatively Charged Quantum Batteries

Abstract

Quantum batteries can exploit quantum resources to enhance energy storage and work extraction, and recent experimental progress has brought their implementation closer to reality. In realistic settings, however, environmental dissipation is unavoidable, making dissipative charging a physically relevant operating regime. Here we investigate ergotropy in dissipatively charged quantum batteries, focusing on interaction-induced work extraction. For two coupled two-level systems (TLSs), we derive exact analytical expressions for the total, coherent, and incoherent ergotropy in both resonant and detuned configurations. We show that, in the resonant case, ergotropy is activated only above a critical coupling associated with an interaction-induced energy-level crossing, whereas detuning enables ergotropy already in the weak-coupling regime. Moreover, quantum coherence, although necessary for coherent work extraction, is not by itself sufficient to guarantee nonzero coherent ergotropy. In the strong-coupling regime, the resonant setup reaches the maximum ergotropy at a finite coupling strength, whereas the detuned setup approaches the same limit only asymptotically. Extending the analysis to a periodic XX spin chain of $N$ TLSs, we analytically derive the finite-temperature coupling threshold for ergotropy activation and show that it scales as $1/N$ in the large-$N$ limit. These results identify frequency detuning, interaction strength, and system size as key control parameters for ergotropy generation in open quantum batteries.