Cold atoms in optical lattices :a Hamiltonian ratchet
  We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods.   The classical dynamics is chaotic and we find the classical diffusion rate $D$ is asymmetric in momentum up to a finite time $t_r$.   The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time $t^* > t_r$. We conclude that the cold atom ratchets require $Db/ \hbar \sim 1$ where b is a small deviation from period-one pulses. 
T.S. Monteiro, P.A. Dando, N.A.C. Hutchings, and M. R. Isherwood