Enhanced Spin Hall effect of light in a prism-free atom-plasmon polariton system based on a three-level medium

We theoretically investigate the Photonic Spin Hall Effect (PSHE) in a prism-free four-layer structure consisting of air, a thin bimetallic film, and an effective three-level Λ system. Driven by probe, coupling, and microwave fields in a closed-loop configuration, the atomic substrate provides dynamically controllable permittivity via electromagnetically induced transparency and coherent population trapping. Solving the steady-state Liouville–von Neumann equations and using a recursive Fresnel coefficient method, we derive the spin-dependent transverse shift of a reflected Gaussian beam. Numerical results, optimized via a genetic algorithm, show that a pure gold film with a thickness of 11.06~nm yields a giant PSHE displacement of 43.321~ at an incidence angle of 46.98^∘, which is approximately $68.46$ times larger than the incident wavelength. Bimetallic stacks exhibit reduced performance due to deviation from optimal impedance-matching conditions. Crucially, the microwave phase enables active tuning of the magnitude and sign of the PSHE displacement. While residual thermal Doppler broadening reduces the peak displacement in a cold atomic ensemble, the shift remains robust for the optimized gold structure, underscoring the viability of the scheme under practical experimental conditions. Furthermore, evaluating the system's performance as a phase sensor reveals an exceptional spatial shift sensitivity of S_δ = 12674.27~/rad and an angular sensitivity of S_θ = 0.64^∘/rad for the optimized pure gold configuration. This work establishes a compact, coupler-free platform for enhancing and controlling spin–orbit interactions in nano-photonic systems, with promising applications in high-resolution metrology and ultra-sensitive sensing.\\