Dynamical instability in kicked Bose-Einstein condensates

Bose-Einstein condensates subject to short pulses “kicks” from standing waves of light represent a nonlinear analog of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability i.e., exponential proliferation of noncondensate particles suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the Bogoliubov spectrum for both the quantum kicked rotor QKR and a variant, the double kicked rotor QKR-2 . We present an analytical model, valid in the limit of weak impulses which correctly gives the scaling properties of the resonances and yields good agreement with mean-field numerics.