Parametric excitation of a Bose-Einstein condensate in a 1D optical lattice

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency Omega drives the parametric excitation of Bogoliubov modes with frequency Omega/2. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stoeferle et al., Phys. Rev. Lett. 92, 130403 (2004).