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We use both mass and internal energy specified rubidium atoms to jointly testthe weak equivalence principle (WEP). We improve the four-wavedouble-diffraction Raman transition method (FWDR) we proposed before to selectatoms with certain mass and angular momentum state, and perform dual-speciesatom interferometer. By combining $^{87}$Rb and $^{85}$Rb atoms with differentangular momenta, we compare the differential gravitational acceleration ofthem, and determine the value of E\"{o}tv\"{o}s parameter, $\eta$, whichmeasures the strength of the violation of WEP. For one case($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statisticaluncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s.With various systematic errors correction, the final value is $\eta=(-4.4 \pm6.7) \times 10^{-10}$. Comparing with the previous WEP test experiments usingatoms, this work gives a new upper limit of WEP violation for $^{87}$Rb and$^{85}$Rb atom pairs.

United test of the equivalence principle at $10^{-10}$ level using mass and internal energy specified atoms