Majorana fermions with spin-orbit coupled cold atom in one-dimensional optical lattices

摘要

We propose an alternative experimental scheme to detect the non-Abelian statistics of the Majorana fermions (MF) with a trapped atomic bosonic gas subject to a spin-orbit coupling in 1D optical lattices. The spin-orbit coupling leads to a faithful simulation of an arbitrary tunable XY spin model, where the anisotropy of the effective spin coupling can be controlled by adjusting the optical potentials, Feshbach resonance, and spin-orbit coupling. MF are created at the ends of the optical lattice segment in topological phase. By controlling the different addressing laser beams, one can move, braid, and exchange them. We also show that the non-Abelian statistics of MF can be demonstrated through distinguishing the states before and after braiding by detecting the parity operator of collective spin states.