Effects of a nonlinear perturbation on dynamical tunneling in cold atoms

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing noninteracting cold atoms in a standing wave of light with a periodical modulated amplitude $A\left(t\right).$ One model is the driven pendulum, recently considered by D.A. Steck, W.H. Oskay, and M.G. Raizen [Science 293, 274 (2001)], and the other is a variant of the well-known kicked rotator model. In absence of the nonlinear perturbation, the system is invariant under some discrete symmetries and quantum dynamical tunneling between symmetric classical islands is found. The presence of nonlinearity destroys tunneling, breaking the symmetries of the system. Finally, further consequences of nonlinearity in the kicked rotator case are considered.