Bloch oscillations and Zener breakdown in an optical lattice

We study the dynamics of ultracold atoms in an optical lattice under consta nt bias. After recapitulating the ideas underlying Bloch oscillations and Z ener's formula for interband transitions, the Bloch-Zener scenario is teste d by means of accurate numerical solutions to the time-dependent Schrodinge r equation. It is shown how two shortcomings of the traditional Zener formu la can be removed: the common weak-binding approximation can be circumvente d by combining Kohn's insight into the structure of complex energy bands wi th the Dykhne-Davis-Pechukas description of transitions in terms of adiabat ic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against th e condensate's nonlinear self-interaction. Yet, under appropriate condition s a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic si gnatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggeste d that such experimentally detectable signatures will play an important rol e in future high-precision experiments aiming at the exploration of many-bo dy dynamics in periodic potentials with condensates in optical lattices.