Emergence of Artificial Photons in an Optical Lattice

We establish the theoretical feasibility of direct analog simulation of the compact $U(1)$ lattice gauge theories in optical lattices with dipolar bosons. We discuss the realizability of the topological Coulomb phase in extended Bose-Hubbard models in several optical lattice geometries. We predict the testable signatures of this emergent phase in noise correlation measurements, thus suggesting the possible emergence of artificial light in optical lattices.

Figure 1

In the left figure, dipolar bosons sit on the sites of the 2D Kagomé lattice, the black circles labeled 1–6. The hexagonal dual lattice, the lattice formed by the centers of the corner-sharing triangles (gray sites), is labeled $a-f$. In the right figure, for simplicity, we show only two corner-sharing tetrahedra of the pyrochlore lattice, with sites shown as spheres.

Figure 2

Expected behavior of the normalized noise correlation function with $q_x$ in the Mott insulating (dashed line) and Coulomb (solid line) phases around the first Brillouin-zone center of the fcc lattice. The core of the Mott insulating peak is suppressed due to the $c|q|$ nonanalyticity provided by the gapless “photon“ at long wavelengths in the Coulomb phase. The behavior, at large $q$, is expected to cross over to that of the Mott insulator. The plot is for a finite sized system with 100 sites along each direction with a small $q$ slope $c=40$ (with the appropriate form factor set to unity) and an arbitrarily chosen cutoff at $q_x=3\pi /500$.