Correlations after a quantum quench in the Bose Hubbard model

Recent experimental advances that allow for the atomic resolution of dynamics for cold atoms in optical lattices call for theory to describe these dynamics. We use the Schwinger-Keldysh technique to study time and space dependent correlations after a quantum quench in the Bose Hubbard model. We focus on the case of time dependent hopping and use a real-time action that allows for the description of both the superfluid and Mott insulating phases to obtain dynamical equations for these correlations. We relate our results to recent experiments.