Parametric amplification of matter waves in periodically translated optical lattices.

We observe the sudden growth of small classes of Bloch waves from atomic Bose-Einstein condensates held in periodically translated optical lattices. The effect is explained by narrowband parametric amplification of Bloch waves from noise, due to phase-matched scattering of atom pairs out of the condensate. Amplification occurs above a well-defined modulation threshold, described by dynamic shaping of single-particle band structure.