Quantum coherence in three-level systems under the combined effect of stark effect and non-linear Kerr medium.

This study investigates the quantum dynamics of three-level Stark-shifted atomic systems under the influence of a Nonlinear Kerr Medium (NLKM), focusing on the interplay between Quantum Fisher Information (QFI), Von Neumann Entropy (VNE), and photon-mediated interactions. By analyzing the temporal evolution of QFI (quantifying parameter estimation precision) and VNE (measuring quantum entanglement (QE), we demonstrate how Kerr nonlinearity (χ), Stark shifts (β), phase (ϕ), and photon numbers govern system behavior. Key findings reveal that lower χ values (e.g., [Formula: see text]) induce oscillatory QFI decay and rapid VNE growth, driven by atomic motion and NLKM interactions, with QFI peaks inversely correlated to VNE dips. Higher [Formula: see text] stabilizes both metrics, suppressing decoherence and entanglement fluctuations. Elevated photon numbers enhance stability by strengthening field-atom correlations, reducing oscillation amplitudes (particularly at low χ), and mitigating quantum fluctuations. The Stark effect (SE) amplifies energy-level shifts, while phase adjustments introduce asymmetries in quantum interference. These results highlight the system's tunability via [Formula: see text], and photon density. They position it as a versatile platform for quantum metrology and information processing, where precision, entanglement stability, and photon-mediated coherence are critical. Kerr interactions suppress long-time coherence and entanglement, while when [Formula: see text], Stark shifts can induce mild, transient quantum correlations. These dynamics are essential for controlling entanglement in cavity QED systems, especially when precise metrological performance is desired.