In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.

submitted to Phys. Rev. E ; 16 pages, 13 figures; figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet/