Abstract
The time-periodic modulation of the self-interaction of a Bose--Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross--Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.
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