Phase diagram of two-species Bose-Einstein condensates in an optical   lattice
  The exact macroscopic wave functions of two-species Bose-Einstein condensates in an optical lattice beyond the tight-binding approximation are studied by solving the coupled nonlinear Schrodinger equations. The phase diagram for superfluid and insulator phases of the condensates is determined analytically according to the macroscopic wave functions of the condensates, which are seen to be traveling matter waves. 
G.-P. Zheng, J.-Q. Liang, and W. M. Liu