We show that non-Abelian lattice gauge fields can be simulated with a single-component ultra-cold atomic gas in an optical-lattice potential. An optical lattice can be viewed as a Bravais lattice with a N -point basis. An atom located at different points of the basis can be considered as a particle in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U( N ) gauge potentials and control a mass of particles that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical-lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of particles . In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.
The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective nondynamical gauge fields. These can be used to generate effective magnetic fields and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with
U(2) symmetry and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a
U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the ground state changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with nonzero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.