Kapitza stabilization of a repulsive Bose-Einstein condensate in an oscillating optical lattice

We show that the Kapitza stabilization can occur in the context of nonlinear quantum fields. Through this phenomenon, an amplitude-modulated lattice can stabilize a Bose-Einstein condensate with repulsive interactions and prevent the spreading for long times. We present a classical and quantum analysis in the framework of Gross-Pitaevskii equation, specifying the parameter region where stabilization occurs. Effects of nonlinearity lead to a significant increase of the stability domain compared with the classical case. Our proposal can be experimentally implemented with current cold atom settings.