Microwave communication based on the cross-phase modulation in an inverted-Y-type Rydberg atomic system

We investigate the microwave-field-induced cross-phase modulation in a room-temperature coherently driven five-level inverted-Y-type system. By solving the optical Bloch equations via the Fourier transformation, we derive two nonlinearly coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we show that the cross-phase modulation-induced phase difference between two components of the probe field is approximately proportional to the microwave field intensity. By choosing a specified probe field frequency, the group velocities for the left- and right-polarized components of the probe field match perfectly so that the phase difference can be detected at the end of the medium, enabling the undistorted detection of the microwave field. Considering the square-pulsed microwave field with a 50% duty cycle, we also demonstrate microwave communication by detecting the cross-phase modulation-induced phase difference.