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In a recent experiment, a two-dimensional spin-orbit coupling (SOC) wasrealized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], whichrepresents an important step forward in the study of synthetic gauge fieldusing cold atoms. In the experiment, it was shown that a Raman-inducedtwo-dimensional SOC exists in the dressed-state basis close to a Dirac point ofthe single-particle spectrum. By contrast, the short-range inter-atomicinteractions of the system are typically expressed in the hyperfine-spin basis.The interplay between synthetic SOC and interactions can potentially lead tointeresting few- and many-body phenomena but has so far eluded theoreticalattention. Here we study in detail properties of two-body bound states of sucha system. We find that, due to the competition between SOC and interaction, thestability region of the two-body bound state is in general reduced.Particularly, the threshold of the lowest two-body bound state is shifted to apositive, SOC-dependent scattering length. Furthermore, the center-of-massmomentum of the lowest two-body bound state becomes nonzero, suggesting theemergence of Fulde-Ferrell pairing states in a many-body setting. Our resultsreveal the critical difference between the experimentally realizedtwo-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in aninteracting system, and paves the way for future characterizations oftopological superfluid states in the experimentally relevant systems.

Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling