Spin-Domain and Superfluid Transition in a shaken optical lattice

Recently, we have developed a resonant lattice shaking technique to induce an effective ferromagnetic transition in a cesium Bose condensate. By phase modulating the optical lattice beam at the frequency near the band gap, we create a double well structure in the energy dispersion. Based on in situ imaging, we observe spatial domains of condensates pinned to one of the two wells. In this work, we extend this technique to form a desired domain structure based by imprinting a potential grating to the sample. We also explore the superfluid transition at finite temperatures in optical lattices.