Coherent ratchets in driven Bose-Einstein condensates.

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.