Interaction of a probe pulse with a "dressed" Bose — Einstein condensate of rarefied atomic gases

Semiclassical equations describing the interaction of a probe pulse with a "dressed" Bose — Einstein condensate of a rarefied atomic gas are proposed. The analytic solution of these equations is obtained for low-intensity pulses. The conditions of the appearance of a diffraction grating from recoil atoms are found. The existence of induced superradiance at the probe-beam frequency is predicted. The pulse propagation velocity in the condensate is determined as a function of its energy. The limits of the applicability of the two-level model of a "dressed" atom are estimated.