Spatial Kramers-Kronig relation and unidirectional light reflection induced by Rydberg interactions

Abstract

Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a sample of homogeneous target atoms and a ring of equally spaced control atoms. This is achieved by establishing an effective two-level configuration for the target atoms in the far-detuned driving regime of both lower and upper transitions while maintaining the maximal Rydberg excitations for the control atoms via an antiblockade driving scheme of the lower and upper transitions. We find, in particular, that it is viable to realize a tunable spatial KK relation supporting asymmetric and even unidirectional reflection for appropriate signal frequencies in a desired range depending on the frequency of a coupling field. Taking a periodic lattice of target atoms instead, the multiple Bragg scattering can be incorporated into the spatial KK relation in order to enhance the nonzero reflectivity yet without breaking the asymmetric or unidirectional reflection.