An atom in a lattice potential undergoes Bloch oscillations when a force is applied: when it reaches the edge of the first Brillouin zone it goes back to the beginning of the Brillouin zone. We set up Bloch oscillations in our BEC by applying a weak optical lattice to the BEC, and then displacing the harmonic magnetic trap holding the BEC so that the BEC is no longer in the center. A schematic of this is shown in part (a) of the figure below. Once displaced, the BEC feels a force due to the trap, and accelerates toward the center. TOF images at different time intervals after the displacement are shown in part (b) of the figure (keep in mind that TOF images show momentum, rather than position). These clearly show the Bloch oscillations; when the BEC reaches a certain momentum (the recoil momentum from absorbing a single photon from the lattice) it is at the end of the Brillouin zone and comes back to the beginning. The magnetic trap continues to accelerate it so that it periodically reaches the edge of the Brillouin zone and goes back to the beginning.
Another way of thinking about this is in terms of a Bragg-reflecting "mirror." When the trap is displaced BEC accelerates toward the center until it reaches one recoil momentum; at this point it is Bragg-reflected by the optical lattice. This acts like a mirror, changing the direction but not the magnitude of the BEC momentum. The BEC now moves away from the center, up the harmonic potential. The potential slows it to a stop, and the BEC turns around and comes back down toward the center. The cycle repeats. In this way, the system can be thought of as a cavity for the BEC, with a mirror on each end: the Bragg-reflecting mirror created by the optical lattice on one end, and the harmonic potential on the other.
We also did 2-D Crank-Nicolson simulations of our system, taking into account mean-field effects. Here are some movies showing the time evolution of the system. Of particular interest is the formation of solitons after a few oscillations; this is especially apparent in the position-space movie.
For more about our work on Bloch oscillations and the Bragg-reflecting atom cavity, see our papers: