Laser control of the singlet-pairing process in an ultracold spinor mixture

In the mixture of ultracold spin-1 atoms of two different species A and B (e.g., $^{23}$Na (A) and $^{87}$Rb (B)), inter-species singlet-pairing process ${\rm A}_{+1}+{\rm B}_{-1}\rightleftharpoons {\rm A}_{-1}+{\rm B}_{+1}$, can be induced by the spin-dependent inter-atomic interaction, where subscript $\pm 1$ denotes the magnetic quantum number. Nevertheless, one cannot isolate this process from other spin-changing processes by tuning the bias real magnetic field. As a result, so far the singlet-pairing process have not been clearly observed in the experiments, and the measurement of the corresponding interaction strength becomes difficult. In this work we propose to control the singlet-pairing process via combining the real magnetic field and a laser-induced species-dependent synthetic magnetic field. With our approach one can significantly enhance this process and simultaneously supperess all other spin-changing processes. We illustrate our approach for both a confined two-atom system and a binary mixture of spinor Bose-Einstein condensates. Our control scheme is helpful for the precise measurement of the weakly singlet-pairing interaction strength and the entanglement generation of two different atoms.