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We present a theoretical analysis of a Bose-Einstein condensate (BEC) enclosed in an optical cavity driven by a modulated external laser beam where the cavity-field variable is adiabatically eliminated. The modulation of the amplitude of the pump laser induces nonlinear resonances and the widespread presence of chaotic oscillations even when repulsive atom-atom interactions are negligible. Close to resonance, varying the modulation amplitude by just a few percent causes abrupt and erratic changes to the output laser intensity with peak power increasing by almost an order of magnitude. We also use a simplified model of the BEC-cavity system that considers only a small number of spatial modes of the BEC to show that, despite the disruptive presence of a modulation in the pump beam, the system can still be considered to be low-dimensional

Chaotic resonances of a Bose-Einstein condensate in a cavity pumped by a modulated optical field