Constraining the spin-gravity coupling effects to the $10^{-10}$-level with dual-species atom interferometers

Spin is one fundamental property of microscopic particles. A lot of theoretical work has postulated the possible coupling between spin and gravitation, which could result in the violation of equivalence principle. In our recent joint mass-and-energy test of the weak equivalence principle with a 10-meter $^{85}$Rb-$^{87}$Rb dual-species atom interferometer, the E${\rm \ddot{o}}$tv${\rm \ddot{o}}$s parameters of four $^{85}$Rb-$^{87}$Rb combinations with specific atomic spin states were measured to the $10^{-10}$-level (\textit{L. Zhou et al., Phys. Rev. A 104, 022822}). Here these experimental results are used to constrain the postulated spin-gravity coupling effects. The bounds on the spin-independent and spin-dependent anomalous passive gravitational mass tensors in L${\rm \ddot{a}}$mmerzahl's model are set to the $10^{-10}$-level, which improves existing bounds by three orders of magnitude. The constraints to the spin-independent electron- and proton-gravity coupling parameters in the gravitational standard-model extension are set to the $10^{-6}\, {\rm GeV}$-level.