We have investigated the dynamics of atom-molecule conversion using a periodically driven spin-boson model both quantum mechanically and semiclassically. The semiclassical dynamics is fully chaotic for small driving frequencies, so that the regular atom-molecule conversion gradually vanishes. In quantum mechanics, however, the periodic conversion takes place at small frequencies since the quantum adiabatic condition is fulfilled. Moreover, it survives for rather larger frequencies that breaks the adiabatic condition, which is understood by considering the so-called dynamical localization. It implies that the periodic atom-molecule conversion is more robust than we expect from the semiclassical approximation. We also show that for much larger frequencies delocalization takes place so that the dynamics becomes diffusive.
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