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Two specific nonlinear effects are studied both theoretically and experimentally: nonlinear Landau-Zener tunneling and instabilities of Bose Einstein condensates in a periodic potential.
Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry. By accelerating a Bose-Einstein condensate in a controlled way across the edge of the Brillouin zone of a 1D optical lattice, we investigate the stability of the condensate in the vicinity of the zone edge. Through an analysis of the visibility of the interference pattern after a time-of-flight and the widths of the interference peaks, we characterize the onset of instability as the acceleration of the lattice is decreased. |