Spin-orbit coupling manipulating composite topological spin textures in atomic-molecular Bose-Einstein condensates

Atomic-molecular Bose-Einstein condensates (BECs) offer brand new opportunities to revolutionize quantum gases and probe the variation of fundamental constants with unprecedented sensitivity. The recent realization of spin-orbit coupling (SOC) in BECs provides a new platform for exploring completely new phenomena unrealizable elsewhere. In this study, we find a way of creating a Rashba-Dresselhaus SOC in atomic-molecular BECs by combining the spin-dependent photoassociation and Raman coupling, which can control the formation and distribution of a different type of topological excitation---carbon-dioxide-like skyrmion. This skyrmion is formed by two half-skyrmions of molecular BECs coupling with one skyrmion of atomic BECs, where the two half-skyrmions locate at both sides of one skyrmion. Carbon-dioxide-like skyrmion can be detected by measuring the vortices structures using the time-of-flight absorption imaging technique in real experiments. Furthermore, we find that SOC can effectively change the occurrence of the Chern number in $k$ space, which causes the creation of topological spin textures from some separated carbon-dioxide-like monomers each with topological charge $\ensuremath{-}2$ to a polymer chain of the skyrmions. This work helps in creating dual SOC atomic-molecular BECs and opens avenues to manipulate topological excitations.