Bloch oscillations (BOs) are one of the most surprising effects in solid state physics. Counter intuitively, the acceleration of particles in a periodic potential does not lead to uniform motion but to an oscillatory motion in position space and thereby to an effective localization. It is commonly believed that BOs prevent the transport of an electron through an ideal crystal and induce a single-particle insulator. Generally, additional relaxation effects, like scattering with lattice defects or with phonons, seem to be necessary to ensure conductance. Using a Bose-Einstein condensate of cesium atoms in 1D optical lattice, we show that there is a surprisingly simple mechanism to create transport in a lattice, even in the absence of scattering.
Bloch oscillations occur if a particle in a periodic potential is subject to a constant force. In a simplified model, the particle is accelerated until it reaches the edge of the first Brillouin zone and acquires a Bragg-reflection. The reflection changes the quasi-velocity of the particle instantly from +vL to -vL (right figure) and the whole process repeats itself periodically. Despite the constant acceleration, the particle shows no net-movement in one-direction (equal shaded areas, top figure). Neglecting any features of the band-structure, the velocity shows the famous saw-tooth like time-evolution that is accompanied by a periodic displacement that extends over just a few lattice sites.
It is possible to periodically drive this system by adding a sinusoidal force:
where Δν corresponds to the deviation of the driving frequency compared to the Bloch frequency νB and Φ represents the phase difference between the Bloch cycle and the drive. A full quantum mechanical description of the system can be found in references [1,2]. Here, we restrict ourselves to a semi-classical analysis that is already sufficient to qualitatively understand the experimental results. The effect of a resonant drive (Δν=0) is very intuitive. The additional force periodically increases or reduces the constant force F0 and thereby distorts the time evolution of the quasi-momentum. While the phase of the resulting Bloch-cycle is shifted, its frequency is still constant νB. Note that there is a net movement for each cycle as the shaded areas are not longer of equal size.
For a driving frequency Δν ≠0 (top figure a, black, red und blue lines), the resulting oscillation is no longer commensurate with the original Bloch cycle and the net-movement per cycle gradually changes (shaded areas figure b). In position space this results in an additional oscillation that exactly matches the shape of the original Bloch oscillation except that these appear on a huge spatial scale of hundreds of lattice sites. These Super-Bloch oscillations result from a beat between the usual BOs and the drive. In reference  we demonstrate those Super-Bloch oscillations can be used to study Bloch oscillations in position space and can be used, by appropriate switching of the detuning or the phase, to engineer transport in a dissipationless system.
top, left to right
Elmar Haller, Johann G. Danzl, Russell Hart, Manfred J. Mark
bottom, left to right:
 Dynamics of interacting atoms in driven tilted optical lattices.
 Theoretical analysis of quantum dynamics in one-dimensional lattices: Wannier-Stark description.
 Inducing Transport in a Dissipation-Free Lattice with Super Bloch Oscillations
Photos for download: ultracold media photos
The experiments are supported by the START-prize of the Bundesministerium für Wissenschaft und Forschung (BMWF) and the Austrian Science Fund (FWF) .
|last change: 21-05-2010 by EH|