In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coup
ling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multi-dimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.
The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a constant, but non-Abelian gauge field, and discuss in the frame of this gauge f
ield the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets.
The Landau levels of cold atomic gases in non-Abelian gauge fields are analyzed. In particular we identify effects on the energy spectrum and density distribution which are purely due to the non-Abelian character of the fields. We investigate in deta
il non-Abelian generalizations of both the Landau and the symmetric gauge. Finally, we discuss how these non-Abelian Landau and symmetric gauges may be generated by means of realistically feasible lasers in a tripod scheme.
