Transient Energy Exchange and Quantum Resources in a Driven Five-Level Kerr Optomechanical Model

Abstract

Abstract We present a finite-time study of energy exchange, quantum correlations, work capacity, and phase sensitivity in a driven hybrid system composed of a five-level atom, a Kerr nonlinear optical mode, and a mechanical oscillator. The atom--field interaction is modulated periodically, while four local Lindblad channels describe two selected atomic transitions together with optical and mechanical damping. Rather than treating the dynamics as a completed heat-engine cycle, we analyze the system as a transient open quantum process and keep the different energetic and information-theoretic quantities clearly separated. The initial optical and mechanical states are taken to be displaced squeezed thermal states, and the atomic subsystem is prepared in a coherent superposition carrying a relative phase. We follow the total energy, reservoir-associated currents, signed driving work, total and reduced entropies, atom--rest negativity, local mechanical ergotropy, and the quantum Fisher information associated with the initial atomic phase. Four parameter sets are considered in order to identify how the Kerr-plus-shift term, atom--field coupling strength, and atomic temperature bias influence the finite-time response. The calculations also track the first-law residual and include selected solver, time-step, and Hilbert-space checks to assess numerical sensitivity without claiming uniform convergence for every parameter set. The results show that stronger atom--field coupling produces the largest sampled atom--rest negativity, but this increase in correlation does not lead to a comparable preservation of the reduced atomic phase quantum Fisher information. Within the employed finite truncation, removing the Kerr-plus-shift term changes the energy balance sufficiently to produce a small positive end-of-window signed work, whereas the other cases give negative final signed work. Because the zero-$\chi$ Hamiltonian has a formal high-occupation instability in the untruncated model and no dedicated enlarged-cutoff test was completed for that case, this small positive value is treated as a result conditional on the adopted finite truncation rather than as a converged engine-performance claim. The mechanical ergotropy remains a local state property and should not be identified with the work exchanged through the external modulation. Taken together, the results show that entanglement, metrological sensitivity, ergotropy, reservoir currents, and driving work respond differently to the same parameter changes. The conclusions therefore apply to the specified phenomenological finite-time model and should not be interpreted as evidence of a completed thermodynamic cycle or of a particular experimental implementation.