Nonlinear polariton waves in an optical double lattice with photo-induced transport of atoms

The process of photo-induced transport of cold atoms in optical lattices is discussed for the case in which the direct tunneling of atoms is suppressed but transport of an atom is possible as a result of simultaneous absorption and reemission of two photons with different energies. Proceeding from the Bose-Hubbard model for two kinds of traps of a one-dimensional optical lattice, a set of equations describing the propagation of an ultrashort pulse of biharmonic radiation accompanied by a transfer of populations of traps of such a double lattice is derived. It was found that, depending on the choice of boundary conditions, there exist two types of stationary solitary waves corresponding to the propagation of a coupled pair of soliton pulses: a pair of bright solitons and a coupled pair of dark and bright solitons