Quantum information metrics of a multi-level atom interacting with an SU(1;1) quantum amplifier system

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Abstract This study investigates the quantum information dynamics of a multi-level atomic system interacting with an SU(1;1) quantum system, focusing on atomic inversion, entropy, coherence, and skew information. The system is specified as a two-level and three-level Λ-type configuration, incorporating multi-mode SU(1;1) quantum systems and the Stark effect. Numerical simulations are performed to solve the time-dependent density matrix equations under varying shift, intensity, and Stark parameters. Results show that increasing the shift stabilizes inversion but raises statistical uncertainty, while greater field intensity amplifies entropy. The Stark amplitude suppresses decoherence and improves quantum information retention. Negativity is used to quantify entanglement between the first two SU(1;1) modes, showing that stronger Stark shifts stabilize entanglement and coherence. Three-level systems consistently outperform two-level ones in preserving coherence and entanglement due to enhanced interference and spectral separation. Eigenvalue analysis reveals the nonlinear structure of three-level systems, explaining their robustness. These findings are supported by recent experiments in SU(1;1) interferometry and Stark-tuned quantum systems, offering insights for quantum sensing, computation, and communication.

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