High-dimensional dynamics of a quantum battery driven by amplified multi-mode fields with stark shifts

Abstract This work presents a high-dimensional quantum battery model based on a V-type multi-level atom interacting with an amplified multi-mode cavity field under controllable Stark shifts. Using a nondimensionalized Hamiltonian and pair-coherent field states, we derive a full density-matrix description that captures the evolution of stored energy, ergotropy, charging efficiency, coherence, and entropy. Our findings show that multi-level quantum batteries outperform two-level systems by leveraging expanded Hilbert spaces to support larger energy storage, richer coherence, and multiple excitation pathways. The charging dynamics are strongly influenced by the field intensity, the shift between paired modes, and the Stark-induced detunings, which collectively determine resonance conditions and interference patterns. A fundamental trade-off emerges: increasing dimensions of quantum battery and field strength enhances energy uptake and coherence, but also raises entropy in the charger field, thereby reducing extractable work. A scaling analysis reveals robust and statistically significant behavioral laws, including quadratic growth of stored energy, exponential decay of efficiency, and exponential increases in coherence and entropy with system dimension. These results outline the energetic and informational limits of high-dimensional quantum batteries and establish a flexible, physically realistic framework for optimizing quantum charging in cavity and circuit QED platforms.