Abstract:
In the recent experiment by S. E. Pollack et. al., PRA 81, 053627 (2010), a Bose-Einstein condensate of $^7$Li has been excited by a harmonic modulation of the atomic s-wave scattering length via Feshbach resonance. Combining an analytical perturbative approach with numerical simulations we analyze the resulting nonlinear dynamics of the system on the mean-field Gross-Pitaevskii level. Our detailed results show the presence of higher harmonics and mode coupling. Most importantly, we also find significant shifts of the col- lective modes frequencies in the resonance region which are due to the nonlinearity of the system dynamics. Finally, we indicate how these frequency shifts could be measured in a future experiment.