Asymmetric and unidirectional reflection based on spatial Kramers-Kronig relation induced by dipole-dipole interactions in Rydberg atoms

For tunable control of asymmetric light reflection, we propose a Rydberg atomic system of the optical response varying in space induced by the long-range position-dependent Rydberg dipole-dipole interaction either in the type of self-van der Waals dipole-dipole interaction or the cross Forster-like dipole-dipole exchange interaction. In such a one-dimensional system consisting of a control atomic driven upon the Rydberg state and a homogeneous target atomic ensemble, the non-localized action from the control atom on the target atoms gradually decreases with the distance between the control and target atoms. Our scheme yields a nonlinear correspondence from a finite spectra range to a finite spatial range of susceptibility via the nonlinear characteristics of Rydberg interaction relative to the position. Therefore, the asymmetric reflection can be induced via the spatial modulation on the target ensemble. In particular, the reflection from one direction can be completely suppressed when the absorption and dispersion parts of the susceptibility are modulated to satisfy the spatial Kramers-Kronig relation in an infinite spectral range. The opposite reflection exhibits a band of a small nonzero reflectivity due to the realistic restriction of the cold atomic density of a relatively small value. Thus, via trapping the target atoms in the optical lattice for the Bragg scattering, we enhance the nonzero reflection obviously and retain the directional reflectionlessness.