Controlled tunneling of cold atoms: from full suppression to strong enhancement

Two recent experiments have demonstrated the phenomenon of dynamical tunneling of cold atoms interacting with standing electromagnetic waves. We show by quantitative calculations that one can achieve a control of the tunneling period over an orders of magnitude range by changing the frequency difference of the waves by about 10% only. In this narrow parameter region, the mechanism of the tunneling oscillations evolves from the two-state to the three-state one. Our calculations demonstrate that the change in the underlying mechanism leads to the dramatic enhancement of the dynamical tunneling. Moreover, a complete suppression of the dynamical tunneling can also be achieved in the cold atom setup.