Nonlinearity-induced effects of Bose-Einstein condensates in periodic potentials

In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy