Spectral and Impedance Matching for Multi-excitation Charging of an Interacting Quantum Battery via an Anharmonic Mediator

Abstract

We investigate a finite-time quantum-battery charging architecture in which a driven two-level working system transfers nonequilibrium resources to an interacting two-qubit battery through a weakly anharmonic three-level mediator. Finite-time driving generates coherence and ergotropy, while excitation-number conservation organizes the transfer into distinct dynamical sectors. The mediator then provides spectrally selective charging channels: its lower transition enables nearly complete single-excitation transfer with negligible residual mediator energy, whereas initial mediator loading activates a cross-matched resonant two-excitation cascade toward the doubly excited battery state. In the latter sector, the mediator anharmonicity compensates the interaction-induced non-equidistance of the battery spectrum, enabling simultaneous resonance of the two transfer channels. At exact double resonance, unequal collective matrix elements impose the analytical bound $P_{\rm max}=8/9$; unit transfer is recovered under the impedance-matching condition $|G_1|=|G_2|$, as confirmed numerically. Detuning scans quantify the spectral tolerance, and the full mixed-state dynamics reveals distinct energy- and ergotropy-transfer profiles. Finite-time compression, thermal reset, and switching work close the cycle-level energy balance to numerical precision. The resulting framework combines nonequilibrium resource generation, spectral matching, impedance matching, and coherent multilevel charging, and provides a basis for extending these principles to collective and many-body quantum batteries.