A technique is proposed for creating nonground-state Bose-Einstein condensates in a trapping potential by means of the temporal modulation of atomic interactions. Applying a time-dependent spatially homogeneous magnetic field modifies the atomic scattering length. An alternating modulation of the scattering length excites the condensate, which, under special conditions, can be transferred to an excited nonlinear coherent mode. It is shown that there occurs a phase-transition-like behavior in the time-averaged population imbalance between the ground and excited states. The application of the suggested technique to realistic experimental conditions is analyzed and it is shown that the considered effect can be realized for experimentally available condensates.
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