Quantum phases in an asymmetric double-well optical lattice

We study the superfluid (SF) and Mott insulator phases of ultracold atoms trapped in a double-well optical lattice. The lattice has an asymmetric double-well geometry along the $x$ axis and single wells along the other axes. We set up the Bose-Hubbard model and evaluate tunneling and atom-atom interaction energies from exact band-structure calculations. Only nearest-neighbor tunneling is considered. This leads to two tunneling energies, $t$ and $J$, to describe hopping along the $x$ axis, and $J_{\perp}$ along the other directions. We assume that the barrier between the double wells is low compared to that between double-well pairs and nearest-neighbor atom-atom interaction can not be ignored. A mean field calculation determines the SF and Mott phase boundaries as a function of lattice parameters and chemical potential $\mu$. The boundary is characterized by an effective tunneling $t_{\rm eff}=t+J$ along the $x$ axis. Moreover, we show that the Mott lobes within the $\mu-t_{\rm eff}$ plane are completely surrounded by SF regions. In future, we will use the results of these simulations to construct effective lattice models where the atom-atom interaction is zero and the interactions are governed by a three-body potential. Such systems might lead to unique many-body ground states.