Mott insulators in plaquettes

We study small systems of strongly interacting ultracold atoms under the influence of gauge potentials and spin-orbit couplings. We use second-order perturbation theory in tunneling, derive an effective theory for the strongly correlated insulating states with one atom per site, and solve it exactly. We find dramatic changes in the level structure and in the amount of degeneracies expected. We also demonstrate the dynamical behavior as the barriers between plaquettes are gradually removed and find potentially high overlap with the resonating valence bond (RVB) state of the larger system.