Engineering dispersion relations: Floquet-Bloch States in a Bose-Einstein Condensate

Bose-Einstein Condensates (BECs) provide a flexible platform to model a wide variety of condensed matter phenomena. To this goal, periodically driven optical lattices are a premier tool to create interesting band structures. By applying both static and moving lattices to a BEC, we investigate Floquet-Bloch states formed in these systems. In our scheme, the $s$ band and the $p_x$ band of a static lattice are coupled through a moving lattice, forming a hybrid $s$-$p_x$ band. The dispersion minimum is shifted away from zero quasimomentum, leading to an artificial gauge field for the atoms. We report our findings as well as future directions of these experiments.