Microwave control of photonic spin Hall effect in atomic system

Abstract

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 $φ\leq π$ 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.