Cold atoms in time dependent optical lattices

Cold atoms in optical lattices provide new avenues for studying iconic condensed matter problems. Using an initially Bose condensed sample of $^87$Rb atoms, we first implement the Bose-Hubbard model (the intensity of the static lattice potential determine the constants in the Bose-Hubbard model). This ``native'' Hamiltonian, with only on-site interactions, exhibits just two phases of matter: insulator and superfluid. Additional phases, such as a supersolid and density wave, are expected when nearest-neighbor interactions are added. Here we show preliminary results where we extend the ``native'' Bose-Hubbard Hamiltonian by rapidly varying the lattice potential.