Bose-Einstein condensate in a bichromatic optical lattice: an exact analytical model

We provide an exact analytical model for the dynamics of a 1D Bose-Einstein condensate loaded in a bichromatic optical lattice. Although a host of exact solutions result from this novel method, we mainly concentrate on the solitonic excitations. The trapping potential and its depth of lattice frustration can be varied by tuning the power and the wavelengths of the two overlaying laser beams. Both attractive and repulsive regimes are thoroughly investigated. In the attractive domain, we obtain bright soliton, which reveals interesting variations with the depth of lattice frustration. Localization of the matter wave density is demonstrated as one of the applications in this regime. In the repulsive domain, dark soliton is obtained when the potential resembles an optical lattice. With appropriate tuning of the potential parameter, the dark soliton becomes modulated with an oscillatory background and gradually transforms to bright solitary trains.