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We investigate the low-energy scattering and bound states of twotwo-component fermionic atoms in pure two-dimensional (2D) and quasi-2Dconfinements with Rashba spin-orbit coupling (SOC). We find that the SOCqualitatively changes the behavior of the 2D scattering amplitude in thelow-energy limit. For quasi-2D systems we obtain the analytic expression forthe effective-2D scattering amplitude and the algebraic equations for thetwo-atom bound state energy. Based on these results, we further derive theeffective 2D interaction potential between two ultracold atoms in the quasi-2Dconfinement with Rashba SOC. These results are crucial for the control of the2D effective physics in quasi-2D geometry via the confinement intensity and theatomic three-dimensional scattering length.

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit coupling