  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.
