  In the presence of a complex classical dynamics associated with a mixed phase
space, a quantum wave function can tunnel between two stable islands through
the chaotic sea, an effect that has no classical counterpart. This phenomenon,
referred to as chaos assisted tunneling, is characterized by large fluctuations
of the tunneling rate when a parameter is varied. To date the full extent of
this effect as well as the associated statistical distribution have never been
observed in a quantum system. Here we analyze the possibility of characterizing
these effects accurately in a cold atom experiment. Using realistic values of
the parameters of an experimental setup, we examine through analytical
estimates and extensive numerical simulations a specific system that can be
implemented with cold atoms, the atomic modulated pendulum. We assess the
efficiency of three possible routes to observe in detail chaos assisted
tunneling properties. Our main conclusion is that due to the fragility of the
symmetry between positive and negative momenta as a function of quasimomentum,
it is very challenging to use tunneling between classical islands centered on
fixed points with opposite momentum. We show that it is more promising to use
islands symmetric in position space, and characterize the regime where it could
be done. The proposed experiment could be realized with current
state-of-the-art technology.
