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1. Title: Quantum Fisher Information of Two-Level Atomic System Subtitle : Under the Influence of Thermal Field, Intrinsic Decoherence , Stark Effect, and Kerr-Like Medium

2. Introduction Importance of quantum systems in information processing. Overview of quantum Fisher information (QFI) and quantum entanglement (QE). Brief introduction to thermal fields, decoherence, Stark effect, and Kerr medium .

3. Quantum Fisher Information (QFI) Definition and significance of QFI in quantum state estimation . Quantum entanglement is a phenomenon where two or more quantum particles become interconnected such that the state of one particle instantly influences the state of the other, regardless of the distance separating them . Role of QFI in understanding quantum dynamics and entanglement . Mathematical formulation of QFI relevant to the study .

4. Quantum Entanglement (QE ) Definition and importance of QE in quantum systems. Different measures of entanglement (e.g., concurrence, negativity). How QE is influenced by decoherence and external fields

5. Effects of Intrinsic Decoherence Impact of intrinsic decoherence on QE and QFI in a thermal field. Expected trends and numerical simulation results. Implications for quantum state manipulation

6. Influence of Kerr Medium Description of Kerr-like medium and its non-linear effects. Influence on the dynamics of QE and QFI. Correlation with von Neumann entropy (VNE).

7. Stark Effect and Atomic Motion Explanation of the Stark effect and its relevance. How atomic motion alters QE and QFI. Periodic behaviors observed in simulations.

8. Anticipated Results Insights into how environmental interactions and decoherence affect QE and QFI. Identification of key characteristics enhancing or diminishing entanglement in dynamic systems. Contributions to the theoretical framework for future research and practical applications.

9. Significance of the Study Contribution to understanding quantum systems' sensitivity to external environments . Implications for quantum information processing and communication technologies . Recommendations for enhancing manipulation and maintenance of quantum states.

10. Methodology Numerical simulations to model the wave function of the two-level atomic system. Systematic alteration of variables: intrinsic decoherence, Kerr medium, Stark effect. Investigating the interaction between QFI and VNE under various environmental settings

11. Conclusion Summary of key findings. Importance of continued research in the field. Invitation for questions and discussions.