Upon increasing the strength of Rashba spin-orbit coupling $\ensuremath{\lambda}$, induced by a synthetic non-Abelian gauge field, a system of fermions at a finite density $\ensuremath{\rho}\ensuremath{\approx}{k}_{F}^{3}$ evolves to a BEC-like state [J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, Phys. Rev. B 84, 014512 (2011)], even in the presence of a weak attractive interaction described by a scattering length
as. The BEC obtained at large spin-orbit coupling ($\ensuremath{\lambda}\ensuremath{\gg}{k}_{F}$) is a condensate of novel bosonic bound pairs of fermions (called ``rashbons'') whose properties are determined solely by the gauge field. Here we investigate the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We show that there is an emergent Galilean invariance at large $\ensuremath{\lambda}$, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett's theorem. We further demonstrate that the rashbon BEC (RBEC) is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length
aR. We show that
aR goes as ${\ensuremath{\lambda}}^{\ensuremath{-}1}$ and is essentially independent of the interaction between the fermions as long as it is nonzero. Analytical results are reported for high-symmetry gauge fields.
We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.