The solution of the Maxwell-Schrodinger equations describing amplification of backwards matter waves the in process of light scattering from a Bose-Einstein condensate of dilute gas is presented. The results obtained in the mean field approximation explain the main features of the effects observed in [1].
We give a general formulation of the semiclassical approach to solving the problem of interaction between a Bose-Einstein condensate of dilute gas and electromagnetic radiation without using the commonly applied mean-field approximation. We suggest variants of the systems of Maxwell-Schrödinger equations whose solution describes such effects as superradiant light scattering, light beam amplification, atomic wave (atomic laser) amplification, induced transparency, and reduction in the group velocity of light.
A semiclassical theory is proposed to describe the light amplification in a Bose—Einstein condensate of a dilute atomic gas observed in [1]. Atomic states with well-defined momenta are taken as a basis of wave functions to derive the Maxwell—Bloch equations for the model of a dilute gas of atoms interacting with electromagnetic field. The evolution of light intensity and populations of coherent atomic states with different recoil momenta is described by solving these equations. The solutions obtained are used to demonstrate theoretically the effects observed in [1].