Simulation of non-Abelian lattice gauge fields with a single-component gas
1 Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński - ulica Reymonta 4, PL-30-059 Kraków, Poland
2 Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński - ulica Reymonta 4, PL-30-059 Kraków, Poland
Received: 8 May 2014
Accepted: 3 July 2014
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.
PACS: 67.85.-d – Ultracold gases, trapped gases / 11.15.Ha – Lattice gauge theory / 73.43.-f – Quantum Hall effects
© EPLA, 2014