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

Abstract

Synthetic non-Abelian gauge fields in cold atom systems produce a Rashba spin-orbit interaction described by a vector $\blam = (λ_x, λ_y, λ_z)$. It was recently shown [Phys. Rev. B 84, 014512 (2011)] that on increasing $λ= |\blam|$, fermions at a finite density $ρ\approx\kf^3$ 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 ${\lambda }_x={\lambda }_y={\lambda }_z=\frac{\lambda }{\sqrt{3}}$.

8+pages, 4 figures

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• Degenerate Quantum Gases with Spin-Orbit Coupling
• Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids
• Short range asymptotic behavior of the wave-functions of interacting spin-half fermionic atoms with spin-orbit coupling: a model study
• BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi gases
• Geometric mass acquisition via quantum metric: an effective band mass theorem for the helicity bands
• Fidelity susceptibility and topological phase transition of a two dimensional spin-orbit coupled Fermi superfluid
• Geometric contribution to the Goldstone mode in spin-orbit coupled Fermi superfluids
• Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings
• Proposed method to realize the $p$-wave superfluid state using a $s$-wave superfluid Fermi gas with a synthetic spin-orbit interaction
• Spin-orbit-coupled atomic Fermi gases in two-dimensional optical lattices in the presence of a Zeeman field
• Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling
• Thermodynamics of spin-orbit-coupled Bose-Einstein condensates
• Unidirectional spin transport of a spin-orbit-coupled atomic matter wave using a moving Dirac $\delta$-potential well
• Fluctuation Theory of Rashba Fermi Gases
• Rashbon bound states associated with a spherical spin-orbit coupling in an ultracold Fermi gas with an $s$-wave interaction
• Non-Galilean response of Rashba coupled Fermi gases
• A universal pairing gap measurement proposal by dynamical excitations in 2D doped attractive Fermi-Hubbard model with spin-orbit coupling
• Feshbach Resonance in a Synthetic Non-Abelian Gauge Field
• Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas