Parametric excitation of a Bose-Einstein condensate in a one-dimensional 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 Stöferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].