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 ( \(\chi\) ), Stark shifts ( \(\beta\) ), phase ( \(\phi\) ), and photon numbers govern system behavior. Key findings reveal that lower \(\chi\) values (e.g., \(\chi =0.3\) ) induce oscillatory QFI decay and rapid VNE growth, driven by atomic motion and NLKM interactions, with QFI peaks inversely correlated to VNE dips. Higher \(\chi (\text{1,3})\) stabilizes both metrics, suppressing decoherence and entanglement fluctuations. Elevated photon numbers enhance stability by strengthening field-atom correlations, reducing oscillation amplitudes (particularly at low \(\chi\) ), 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 \(\chi , \beta . \phi\) , 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 \(\chi =0\) , 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.
