Title: Polarization dependent non-Hermitian atomic grating controlled by dipole blockade effect

Abstract: We propose a theoretical scheme for a non-Hermitian atomic grating within an ultra-cold rubidium-87 ($^{87}Rb$) atomic ensemble. The grating's diffraction properties depend on the polarization states of incident photons and are controlled non-locally through Rydberg interactions. Multiple types of polarization-dependent diffraction modes are generated, benefiting from no crosstalk atomic transition channels based on transition selection rules. Those polarization-dependent diffraction modes can be switched using dynamic optical pulse trains, exploiting the Rydberg blockade effect, and are tunable by non-Hermitian optical modulation. Our work will advance the application of asymmetric optical scattering by utilizing the polarization degree of freedom within continuous media and benefit the application of versatile non-Hermitian/asymmetric optical devices.