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

## TL;DR

This study tests the mean-field prediction that the properties of lattice-trapped Bose gases are insensitive to lattice geometry when scaled by the coordination number, by comparing superfluid to Mott insulator transitions in kagome and triangular lattices.

## Contribution

The paper provides experimental validation of mean-field scaling predictions across different 2D lattice geometries in ultracold Bose gases.

## Key findings

- Coherent fraction lower in kagome lattice than in triangular lattice at same parameters.
- Experimental data agrees quantitatively with mean-field scaling predictions.
- Observed dynamics of gas response to lattice geometry change and hole doping.

## Abstract

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 $^{87}$Rb 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.