We report the observation of harmonic generation and strong nonlinear coupling of two collective modes of a condensed gas of rubidium atoms. Using a modified TOP trap we changed the trap anisotropy to a value where the frequency of the m=0 high-lying mode corresponds to twice the frequency of the m=0 low-lying mode, thus leading to strong nonlinear coupling between these modes. By changing the anisotropy of the trap and exciting the low-lying mode we observed significant frequency shifts of this fundamental mode and also the generation of its second harmonic.
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