Microwave control of photonic spin Hall effect in atomic system

The photonic Spin Hall Effect (SHE) causes a polarization-dependent transverse shift of light at an interface. There is a significant research interest in controlling and enhancing the photonic SHE. In this paper, we theoretically investigate the microwave field control of the photonic SHE in a closed-loop Λ-type atomic system. We demonstrate that both the magnitude and angular position of the photonic SHE can be controlled by varying the relative phase φ between the driving optical fields and the strength of the microwave coupling Ω_μ. At zero probe field detuning $Δ_p = 0$ and φ=0,π, the photonic SHE magnitude reaches to upper limit equal to the half of the incident beam waist, and remains largely unaffected by the microwave strength Ω_μ, but its angular position shifts linearly with increasing Ω_μ. At intermediate phases, especially at φ= π/2, the magnitude of the photonic SHE exponentially decreases with the increase of Ω_μ. Interestingly, we observed microwave-controlled switching of photonic SHE by tuning the relative phase φ at an optimized value of Ω_μ and Ω_c. In contrast, at Δ_p = pm Ω_c, a maximum photonic SHE equal to half of the incident beam waist occurs at φleq π and Ω_μ geq Ω_p, where both real and imaginary parts of the susceptibility vanish, yielding a unit refractive index. Our results may have potential applications in microwave quantum sensing and quantum optical switches based on the photonic SHE.