Mode locking of a driven Bose-Einstein condensate.

We consider the dynamics of a driven Bose-Einstein condensate with positive scattering length. Employing an accustomed variational treatment we show that when the scattering length is time modulated as a{1+epsilonsin[omega(t)t]}, where omega(t) increases linearly in time, i.e., omega(t)=gammat, the response frequency of the condensate locks to the eigenfrequency for small values of epsilon and gamma. A simple analytical model is presented which explains this phenomenon by mapping it to an auto-resonance, i.e., close to resonance the reduced equations describing the collective behavior of the condensate are equivalent to those of a virtual particle trapped in a finite-depth energy minimum of an effective potential.