In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases that depends on the density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to both the direct Raman process and the interaction-assisted Raman process. The interaction-assisted Raman process depends on the density of atoms. These two processes have opposite effects in terms 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. During this crossover, 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 reflectional symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method may pave a way to novel phenomena in the density-dependent spin-orbit coupling gauge field with intrinsic dynamics.

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• Bose-Einstein condensates
• Cold atoms & matter waves
• Fermi gases
• Spin-orbit coupling