  Motivated by recent experiments, we investigate particle emission from a
Bose-Einstein condensate in a one-dimensional lattice, where the interaction
strength is periodically modulated. The modulated interactions parametrically
excite a collective mode, leading to density oscillations. These collective
oscillations in turn drive particle emission. This multistep process amplifies
the drive, producing larger particle jets. We find that the amplitude
dependence of the emission rate has a characteristic threshold behavior, as
seen in experiments.
