Optical Kagome Lattice for Ultracold Atoms with Nearest Neighbor Interactions

We propose a scheme to implement an optical kagome lattice for ultracold atoms with controllable $s$-wave interactions between nearest neighbor sites and a gauge potential. The atoms occupy three different internal atomic levels with electromagnetically induced coupling between the levels. We show that by appropriately shifting the triangular lattice potentials, experienced by atoms in different levels, the kagome lattice can be realized using only two standing waves, generating a highly frustrated quantum system for the atoms.

Figure 1

Left: In the kagome lattice the atoms occupy three electronic ground states with a common excited state. The frequencies of the two lattice lasers are tuned between the atomic resonance frequencies in such a way that ${\omega }_3>{\omega }_{\alpha }>{\omega }_2>{\omega }_{\beta }>{\omega }_1$. The polarization components of the lattice lasers that couple to each individual transition are indicated. Right: Atoms in each of the three internal levels $|j⟩$ ($j=1,2,3$) experience an equilateral triangular lattice potential. These lattices are shifted with respect to each other, so that the lattice site occupied by the atoms in $|2⟩$ ($|3⟩$) is at the midpoint of the triangle side of $|1⟩$ defined by the unit vector ${\mathbf{k}}_{\beta }/k=({\widehat{\mathbf{e}}}_y-\sqrt{3}{\widehat{\mathbf{e}}}_z)/2$ (${\widehat{\mathbf{e}}}_z$). Each site has four NN sites, so that, e.g., the site of $|1⟩$ has two NN sites of $|2⟩$ and two of $|3⟩$.