Fermions in synthetic non-Abelian gauge fields

The ability of cold atoms to simulate condensed-matter systems has
been bolstered by the recent spectacular experimental advances in the
generation of synthetic gauge fields.  After a brief review of ideas
for the generation of synthetic non-Abelian gauge fields, I shall
discuss the physics of interacting fermions in their presence. Such
gauge fields induce a generalized spin-orbit interaction for the two
component fermions. I shall demonstrate that on increasing the
strength of the spin-orbit coupling, a BCS superfluid that is realized
in the presence of weak attraction in the absence of the gauge field,
is driven to BEC state. The BEC state is a condensate of a new kind of
nematic bosons, which we call "rashbons", whose properties are
determined solely by the gauge field and not by the strength of the
attraction between the fermions. The rashbon-BEC is shown to have a
transition temperature of the order of the Fermi temperature
suggesting a route to enhancing the transition temperature in weakly
attracting systems using spin-orbit interaction. I shall then show
that the rashbon-BEC is described by a Bogoliubov theory and estimate
that the rashbon-rashbon scattering length which is shown to be
*independent* of the scattering length between the constituent
fermions. Finally, I will make a proposal of using a non-Abelian gauge
field in a conjunction with another potential for the realization of
interesting condensed matter Hamiltonians such as that due to a
magnetic monopole.