Controlled unidirectional reflection in cold atoms via the spatial Kramers-Kronig relation

We propose a model for realizing frequency-dependent spatial variations of the probe susceptibility in cold atomic sample. It is found that usual Kramers-Kronig (KK) relation between real and imaginary parts frequency domain can be mapped into space as far detuned control field intensity linearly varied used. This non-Hermitian medium exhibits then unidirectional reflectionless band photons incident from either left or right sample end. special interest we tune well choose direction corresponding to vanishing reflectivity by changing, respectively, frequency. The nonzero other typically small realistic densities, but largely enhanced incorporating Bragg scattering KK so achieve high contrast.