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 $\ensuremath{\Omega}$ drives the parametric excitation of Bogoliubov modes with frequency $\ensuremath{\Omega}∕2$. 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 St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

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