Density Dependent Spin-Orbit Coupling in Degenerate Quantum Gases

In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases whose format and strength depend on density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to the direct Raman process and the interaction assisted Raman process, and the latter depends on density of atoms. These two processes have opposite effects in term of spin-momentum locking and compete with each other. As the interaction modulation increases, the system undergoes a crossover from the direct Raman process dominated regime to the interaction assisted Raman process dominated regime. For this crossover, we show that for bosons, both the condensate momentum and the chirality of condensate wave function change sign, and for fermions, the Fermi surface distortion is inverted. We highlight that there exists an emergent spatial reflection symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method paves a way to novel phenomena in a non-abelian gauge field with intrinsic dynamics.