Abstract
Topological states have received much attention for their exotic properties which may be useful for building a topological quantum computer. Various promising proposals exist for realizing such states. One of them is to use Majorana zero mode within vortices of a p+ip superfluid. Unlike bosons or fermions, under exchange of vortices, these Majorana mode obeys the non-abelian statistics. So far, such Majarana zero mode has not been unambiguously identified in realistic experiment.
In this talk, we propose to investigate another promising candidate system, namely, ultracold two component Fermi gases with synthetic spin-orbit couplings. In particular, we are interested in the fate of majorana mode (if exist) within the vortex core when the system is tuned from a weak coupling BCS superfluid to a strong coupling Bose-Einstein condensate of di-fermionic molecules. Possible experimental signatures of Majorana mode will be also discussed.