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We show the existence of spin-Hall effect of light (SHEL) in an atomic mediumwhich is made anisotropic via electromagnetically induced transparency. Themedium is made birefringent by applying an additional linearly polarizedcoupling light beam. The refractive index and the orientation of the opticsaxis are controlled by the coupling beam. We show that after transmitting theatomic medium, a linearly polarized probe light beam splits into its two spincomponents by opposite transverse shifts. With proper choice of parameters andatomic density of about $2.5\times10^{17}\,\mathrm{m}^{-3}$, the shifts areabout the order of wavelength and can be larger than the wavelength byincreasing the atomic density. We propose a novel measurement scheme based on abalanced homodyne detection (BHD). By properly choosing the polarization,phase, and transverse mode of the local oscillator of the BHD, one canindependently measure (i) the SHEL shifts of the two spin components; (ii) thespatial and angular shifts; (iii) the transverse and longitudinal shifts. Themeasurement can reach the quantum limit of precision by detecting signals atthe modulation frequency of the electro-optic modulator used to modulate theinput probe beam. The precision is estimated to be at the nanometer levellimited by the quantum noise.

Controllable spin-Hall and related effects of light in an atomic medium via coupling fields