Collision of discrete breathers in two-species Bose-Einstein condensates in optical lattices

The properties of Bose-Einstein condensates (BEC) can be studied and controlled effectively when trapped in optical lattices. In the limit of tight binding, BEC in optical lattices are well described by the discrete nonlinear Schrödinger equation (DNLSE). Spatially localised modes of excitations, known as discrete breathers or lattice solitons, can occur in the DNLSE [1]. These have been shown to evolve from initial conditions of Gaussian wave-packets [1, 2]. Using this method with the addition of an initial momentum, mobile breathers that travel across the lattice with a constant velocity can also be formed [1, 2]. With a second atomic species in the lattice, the interaction of the condensates is described by two coupled DNLSE: