  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.
