Nonlinear excitations in arrays of Bose-Einstein condensates

The dynamics of localized excitations in an array of Bose-Einstein condensates (BECs) is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distribution localized on very few lattice sites (intrinsic localized modes), as well as atomic population distributions involving many lattice sites (envelope solitons). is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunneling and nonlinearity-induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and nonzero backgrounds, We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable, We also show that bright solitons and excitations of shock-wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that a BEC array with negative scattering length in the presence of linear potentials can display collapse.