Simulating ($2+1$)-Dimensional Lattice QED with Dynamical Matter Using Ultracold Atoms

We suggest a method to simulate compact quantum electrodynamics using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in $2+1$ dimensions. This allows us to test the dynamical effects of confinement as well as the deformations and breaking of two-dimensional flux loops, and to observe the Wilson-loop area law.

Figure 1

The simulating lattice. Every link is occupied by a single boson [yellow (light) circles] and every vertex by either zero, one, or two fermions [blue (dark) circles].

Figure 2

Examples of gauge field and matter dynamics, as explained in the text, for an initial state of a single flux loop (a). Panels (b)–(f) show possible outcomes of first-order processes. Panels (b)–(d) result from operations of $H_B$: (b) loop decreasing, (c) loop increasing, (d) exciting a nonconnected plaquette. Panels (e)–(f) result from operations of $H_D$: (e) loop breaking and creation of two charges, (f) creation of a meson outside the loop.

Figure 3

Description of the area-law experiment in space-time, as described in the text. The interference phase depends on the green (darker) area.