Coupling between collective excitations of a Bose-Einstein condensate and modulated interactions

We investigate collective excitations of a Bose-Einstein condensate in the presence of temporal modulation of repulsive interactions, and analytically demonstrate that the modulated interaction can drive the condensate to oscillate with the external modulation frequency, and that the interaction couples with the eigen modes of the condensate collective excitations, which was previously considered to be independent of interaction. When the external modulation frequency approaches or is far away from the eigen frequency of the density monopole mode, the condensate shows resonant or beating behaviour.