Realization of simultaneously parity-time-symmetric and parity-time-antisymmetric susceptibilities along the longitudinal direction in atomic systems with all optical controls.

We propose an all-optical-control scheme to simultaneously realize parity-time (𝒫𝒯)-symmetric and 𝒫𝒯-antisymmetric susceptibilities along the propagation direction of light by applying an external magnetic field. Through the light-atom interaction within a double-Λ configuration, the resulting position-dependent susceptibilities for the interacting fields can be manipulated through the relative phase between them. In particular, for the probe field, one can switch its refractive index from the 𝒫𝒯-symmetry to 𝒫𝒯-antisymmetry by just varying the phase. Based on the quantum interference among transition channels in a closed loop, analytical formulas are also derived to illustrate the conditions for 𝒫𝒯-symmetry and 𝒫𝒯-antisymmetry.