## Collective excitations across the BCS-BEC crossover induced by a synthetic Rashba spin-orbit coupling    [PDF]

Jayantha P. Vyasanakere, Vijay B. Shenoy
Synthetic non-Abelian gauge fields in cold atom systems produce a Rashba
spin-orbit interaction described by a vector $\blam = (\lambda_x, \lambda_y, \lambda_z)$. It was recently shown [Phys. Rev. B 84, 014512 (2011)] that on
increasing $\lambda = |\blam|$, fermions at a finite density $\rho\approx\kf^3$
evolve to a BEC like state even in the presence of a weak attractive
interaction (described by a scattering length $\as$). The BEC obtained at large
spin-orbit coupling ($\lambda \gg k_F$) is a condensate of rashbons -- novel
bosonic bound pairs of fermions whose properties are determined solely by the
gauge field. Here we study the collective excitations of such superfluids by
constructing a Gaussian theory using functional integral methods. We derive
explicit expressions for superfluid phase stiffness, sound speed and mass of
the Anderson-Higgs boson that are valid for any $\blam$ and scattering length.
We find that at finite $\lambda$, the phase stiffness is always lower than that
set by the density of particles, consistent with earlier work[arXiv:1110.3565]
which attributed this to the lack of Galilean invariance of the system at
finite $\lambda$. We show that there is an emergent Galilean invariance at
large $\lambda$, and the phase stiffness is determined by the rashbon density
and mass, consistent with Leggett's theorem. We further demonstrate that the
rashbon BEC state is a superfluid of anisotropic rashbons interacting via a
contact interaction characterized by a rashbon-rashbon scattering length $a_R$.
We show that $a_R$ goes as $\lambda^{-1}$ and is essentially {\em independent}
of the scattering length between the fermions as long as it is nonzero.
Analytical results are presented for a rashbon BEC obtained in a spherical
gauge field with $\lambda_x = \lambda_y = \lambda_z = \frac{\lambda}{\sqrt{3}}$.
View original: http://arxiv.org/abs/1201.5332