Confinement and Lattice Quantum-Electrodynamic Electric Flux Tubes Simulated with Ultracold Atoms

We propose a method for simulating $(2+1)\mathrm{D}$ compact lattice quantum-electrodynamics, using ultracold atoms in optical lattices. In our model local Bose-Einstein condensates’ (BECs) phases correspond to the electromagnetic vector potential, and the local number operators represent the conjugate electric field. The well-known gauge-invariant Kogut-Susskind Hamiltonian is obtained as an effective low-energy theory. The field is then coupled to external static charges. We show that in the strong coupling limit this gives rise to “electric flux tubes” and to confinement. This can be observed by measuring the local density deviations of the BECs, and is expected to hold even, to some extent, outside the perturbative calculable regime.

Figure 1

Left: Structure of the lattice. The different condensate species are colored in four colors; the colored boxes represent the links (condensates), and there the localized wave functions are concentrated. At the vertex (symbolized by a cube) the wave functions of the neighboring links overlap and these are the only overlap integrals which are not negligible. Right: A close-up picture of a single vertex, showing the various interaction parts of the Hamiltonian—scattering and hopping.

Figure 2

An example of the charge and flux configurations, for $R=2$. The different colors represent the condensate species. The upper couple of charges are with QED quantum numbers, and the lower couple with BEC local number deviations quantum numbers. Such a flux tube can be embedded, in the absence of other charges, in a lattice whose other links carry $E=0$.