Chaotic and Stable Regimes of Quantum Entanglement Under Stark Modulation and Detuning Without Rotating Wave Approximation

This work presents a comprehensive study of atom–…eld interactions by examining how subtle variations in key parameters a⁄ect quantum dynamics. In our investigation, the time-dependent Stark shift (SS) is systematically varied from low (approximately 0:3) to high (around 3) values. Under weak Stark modulation, the system closely mirrors the traditional Jaynes–Cummings model, displaying smooth Rabi oscillations and modest ‡uctuations in quantum measures such as the Quantum Fisher Information (QFI), Von Neumann Entropy (VNE), and Negativity (Neg). As the Stark parameter increases, the atom and …eld are driven in and out of resonance more abruptly, leading to rapid, high-amplitude bursts of quantum entanglement (QE) and marked shifts in the Geometric Phase. The study further explores the role of a small nonzero initial phase ( = =4), which subtly alters the interference between the atom and …eld. This additional phase results in slight shifts in the timing and magnitude of QE peaks when compared with a purely real initial state. Additionally, the incorporation of detuning and atomic motion introduces o⁄-resonant e⁄ects and vibrational sidebands, respectively. These elements further complicate the energy exchange process and enrich the overall dynamics. Overall, the results underscore that even slight modi…cations in external parameters can lead to signi…cant variations in QE behavior and phase evolution, o⁄ering valuable insights for the …ne-tuning of quantum systems in advanced technological application.