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 $\omega_m$ drives the parametric excitation of Bogoliubov modes with frequency $\omega_m/2$. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and of the condensate size after free expansion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stoeferle et al., Phys. Rev. Lett. 92, 130403 (2004), and show that the presence of a large condensate depletion is not essential to explain the observed broad response.