Enhanced photonic spin Hall effect in atomic-ensemble-based cavity optomechanics

Cavity optomechanics, which investigates the interaction of electromagnetic fields with mechanical resonators via radiation pressure, offers an intriguing perspective on how quantum mechanical concepts materialize at macroscopic scales. Here, we present a novel approach to investigate the photonic spin Hall effect (SHE) in a multilayered system, by introducing $\mathrm{\ensuremath{\Lambda}}\text{\ensuremath{-}}\mathrm{type}$ three-level coherent atomic medium inside a mirror and dielectric slab, causing an optomechanical effect on light incidence. Unlike typical photonic SHE systems that rely on fixed material setup, we demonstrate that photon-phonon coupling in an optomechanical cavity permits dynamic manipulation of the spin-orbit interaction of light. We employ the transfer matrix approach for computing the ratio of reflection coefficients for the TM and TE components, illustrating the manipulation of the transverse shift of reflected light from positive to negative near the Brewster angle. Further, we demonstrate that manipulating important variables such as photon-phonon, atom-photon coupling strengths, and atomic Rabi frequency can impact both the magnitude and angular position of the photonic SHE. This optomechanical interaction has significant advantages over conventional approaches because it allows for real-time tuning of the SHE, increasing its potential for applications in optical sensing, spintronic devices, and quantum information processing. Our findings pave the way for further research into dynamically controlled photonic spin-dependent effects, offering a diverse platform to advance light manipulation.