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We present our experimental investigations on the subject ofnonlinearity-modified Bloch-oscillations and of nonlinear Landau-Zenertunneling between two energy bands in a rubidium Bose Einstein condensate in anaccelerated periodic potential. Nonlinearity introduces an asymmetry inLandau-Zener tunneling. We also present measurements of resonantly enhancedtunneling between the Wannier-Stark energy levels for Bose-Einstein condensatesloaded into an optical lattice.

Bose-Einstein condensates in 1D optical lattices: nonlinearity and Wannier-Stark spectra