  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.
