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.
Abstract In this work we study the effect of density-dependent gauge field on the collective dynamics of a harmonically trapped Bose–Einstein condensate (BEC), beyond the linear response regime. The density-dependent gauge field, as a backaction of the condensate, can in turn affect the condensate dynamics, resulting in highly nonlinear equations of motion. The dipole and breathing oscillations of the condensate along the direction of gauge field are coupled by this field. We find that, in the presence of this coupling, the collective motion of a quasi-one-dimensional condensate is still regular, i.e., periodic or quasiperiodic. In contrast, for a quasi-two-dimensional condensate, the collective dynamics of the condensate can become chaotic, when the density-dependent gauge field is strong. The mechanism is that the gauge field can also induce a Hall effect, manifested as an additional coupling between dipole and breathing oscillations in perpendicular direction, and chaotic motion is resulted from the interplay between these oscillations. Our findings reveal an important effect of dynamical gauge field on the nonlinear dynamics of a BEC.