Multichannel Molecular State and Rectified Short-range Boundary Condition for Spin-orbit Coupled Ultracold Fermions Near p-wave Resonances

We study the interplay of spin-orbit coupling (SOC) and strong p-wave interaction to the scattering property of spin-1/2 ultracold Fermi gases. Based on a two-channel square-well potential generating p-wave resonance, we show that the presence of an isotropic SOC, even for its length much longer than the potential range, can greatly modify the p-wave short-range boundary condition(BC). As a result, the conventional p-wave BC cannot predict the induced molecules near p-wave resonance, which can be fully destroyed to vanish due to strong interference between s- and p-wave channels. By analyzing the intrinsic reasons for the breakdown of conventional BC, we propose a new p-wave BC that can excellently reproduce the exact molecule solutions and also equally apply for a wide class of single-particle potentials besides SOC. This work reveals the significant effect of SOC to both the short- and long-range properties of fermions near p-wave resonance, paving the way for future exploring interesting few- and many-body physics in such system.