  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.
