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The mean-field treatment of the Bose-Hubbard model predicts properties oflattice-trapped gases to be insensitive to the specific lattice geometry oncesystem energies are scaled by the lattice coordination number $z$. We test thisscaling directly by comparing coherence properties of $^{87}$Rb gases that aredriven across the superfluid to Mott insulator transition within opticallattices of either the kagome ($z=4$) or the triangular ($z=6$) geometries. Thecoherent fraction measured for atoms in the kagome lattice is lower than forthose in a triangular lattice with the same interaction and tunneling energies.A comparison of measurements from both lattices agrees quantitatively with thescaling prediction. We also study the response of the gas to a change inlattice geometry, and observe the dynamics as a strongly interactingkagome-lattice gas is suddenly "hole-doped" by introducing the additional sitesof the triangular lattice.

Mean-field scaling of the superfluid to Mott insulator transition in a 2D optical superlattice