Geometric Phases generated by the non-trivial spatial topology of static vector fields coupled to a neutral spin-endowed particle. Application to 171Yb atoms trapped in a 2D optical lattice

We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which recasts the magnetic spin interaction under a diagonal form. Rewriting the kinetic term in the "rotated" frame requires the introduction of non-Abelian covariant derivatives, involving the gradients of the Euler angles which define the orientation of the local field. Within the rotated frame, we have built a perturbation scheme,assuming that the longitudinal non-Abelian field component dominates the transverse ones, to be evaluated to second-order. The geometry embedded in the longitudinal gauge vector field and its curl, the geometric magnetic field, is described by the associated Aharonov-Bohm phase. As an illustration, we study the physics of cold 171Yb atoms dressed by two sets of circularly polarized beams, forming square or triangular 2D optical lattices. The geometric field is computed explicitly from the Euler angles. The magnitude of 2nd-order corrections due to transverse fields can be reduced to the percent level by a choice of light intensity which keeps the dressed atom loss rate below 5 s^{-1}. An auxiliary optical lattice confines the atoms within 2D domains where the geometric field is pointing upward.Comment: 12 pages, 4 figures. Comments and one figure added about the effect of the additional scalar potential (sec. V.B). To be published in J. Phys. A:Math. Theo

Optical Flux Lattices for Two-Photon Dressed States

We describe a simple scheme by which "optical flux lattices" can be implemented in ultracold atomic gases using two-photon dressed states. This scheme can be applied, for example, to the ground state hyperfine levels of commonly used atomic species. The resulting flux lattices simulate a magnetic field with high mean flux density, and have low energy bands analogous to the lowest Landau level. We show that in practical cases the atomic motion significantly deviates from the adiabatic following of one dressed state, and that this can lead to significant interactions even for fermions occupying a single band. Our scheme allows experiments on cold atomic gases to explore strong correlation phenomena related to the fractional quantum Hall effect, both for fermions and bosons.Comment: 6 page