Exploring the Charging Dynamics of a Deformed Quantum Battery

This manuscript delineates a rigorous theoretical framework and mathematical derivation for a Quantum Battery (QB) constituted by an atomic ensemble interacting with a nonlinear radiation field. We extend the paradigmatic Dicke model by incorporating a Kerr‐type nonlinearity through an algebraic ‐deformation of the Heisenberg–Weyl algebra. By resolving the time‐dependent Schrödinger equation, we explicate the system of coupled ordinary differential equations that govern the temporal evolution of the state amplitudes. Furthermore, we formulate the reduced density operator for the battery subsystem to evaluate critical thermodynamic figures of merit, specifically distinguishing between total stored energy and ergotropy (extractable work) in the presence of quantum correlations. Our results elucidate the interplay between optical nonlinearity, collective atomic effects, and the thermodynamic efficiency of the charging protocol.