Quantum Fisher Information of Three-Level Atom Under the Combined Influence of the Non-Linear Kerr Medium and the Stark Effect

We explore the dynamics of Quantum Fisher Information (QFI) and Von Neumann Entropy (VNE) in three-level stationary and moving Stark-shifted atomic systems influenced by a Nonlinear Kerr Medium (NLKM). QFI, which measures coherence and sensitivity to parameter changes, decreases over time due to decoherence, with slower decay at higher nonlinearity values. VNE, an indicator of quantum entanglement, increases over time, with stronger growth observed at lower nonlinearity valueThe Stark effect, caused by an external electric field, introduces energy level shifts that result in oscillatory behavior in both QFI and VNE. Stronger electric fields amplify these oscillations, enhancing sensitivity and entanglement dynamics. The system's phase significantly impacts its behavior, with symmetric patterns emerging at zero phase and more complex dynamics occurring at other phase values. In moving systems, atomic motion interacts with NLKM and Stark effects to produce periodic modulations in QFI and VNE. Lower nonlinearity values lead to pronounced oscillations, reflecting stronger quantum interactions, while higher values stabilize coherence. Peaks in QFI often align with dips in VNE, indicating a trade-off between precision and entanglement. Transient spikes in VNE highlight moments of enhanced quantum entanglement, while high QFI values signify robust coherence, critical for precision measurements. This study demonstrates the tunability of quantum systems through external field strength, nonlinearity, and phase, providing a framework for optimizing quantum sensing and exploring the fundamental dynamics of coherence and entanglement in quantum systems.