Dynamical instabilities of Bose-Einstein condensates at the band edge in one-dimensional optical lattices

We present a joint theoretical and experimental study of the dynamical instability of a Bose-Einstein condensate at the band edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and undertake a thorough theoretical study of the dynamical instability in systems of different dimensionality. We find spontaneous scattering is an important part of this process, and thus the Gross-Pitaevskii equation is unable to accurately predict the dynamics in this system. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and heating that are observed in the laboratory, and we find good agreement with the experimental results.