Macroscopic quantum self-trapping in dynamical tunneling

It is well known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunneling between the two sites. Here we find analogous behavior in the dynamical tunneling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunneling between the resonances, but with an increasing period as compared to the noninteracting system. For nonlinearities above a critical value we generally observe that the tunneling shuts down. However, for certain regimes of modulation parameters we find that dynamical tunneling reemerges for large enough nonlinearities, an effect not present in spatial double-well tunneling. We develop a two-mode model in good agreement with full numerical simulations over a wide range of parameters, which allows the suppression of tunneling to be attributed to macroscopic quantum self-trapping.