Spatial patterns in optical lattices submitted to gauge potentialsN. Goldman
Center for Nonlinear Phenomena and Complex Systems - Université Libre de Bruxelles (U.L.B.) - Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
received 22 July 2007; accepted in final form 22 August 2007; published October 2007
published online 12 September 2007
We study the vortex formation in optical lattices submitted to artificial gauge potentials. We compute the superfluid density for Abelian and non-Abelian gauge potentials with a mean-field approach of the Bose-Hubbard model and we determine the rule describing the number of vortices as a function of the effective magnetic flux. This simple rule is represented by a remarkably rich figure that represents the superfluid density as a function of the flux. The phenomena which emanate from this work should be observed experimentally in optical lattices within which atom tunneling is laser-assisted and described by commutative or non-commutative tunneling operators.
03.75.Lm - Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations.
05.30.Jp - Boson systems.
67.40.Db - Quantum statistical theory; ground state, elementary excitations.
© Europhysics Letters Association 2007