Mean-field scaling of the superfluid to Mott insulator transition in a two-dimensional optical superlattice

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of 87Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z= 4) or the triangular (z= 6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly “hole-doped” by introducing the additional sites of the triangular lattice.The Bose-Hubbard model describes bosons confined to a lattice, and predicts a low-temperature phase transition between superfluid and Mott insulating states that is driven by on-site interactions [1]. A mean-field treatment of this model neglects non-local correlations and specifies that system properties such as particle number (n), superfluid number (nsf), and entropy (s) per lattice site depend on the system’s characteristic energies–the chemical potential (µ), on-site interaction energy (U), and thermal energy (τ= kBT)–once they are scaled by zJ, where z is the lattice coordination number and J is the tunneling energy. Aside from the inclusion of z, the mean-field theory is insensitive to the lattice geometry. Treatments that consider non …