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

Abstract

We use both mass and internal energy specified rubidium atoms to jointly test the weak equivalence principle (WEP). We improve the four-wave double-diffraction Raman transition method (FWDR) we proposed before to select atoms with certain mass and angular momentum state, and perform dual-species atom interferometer. By combining ${}^{87}$Rb and ${}^{85}$Rb atoms with different angular momenta, we compare the differential gravitational acceleration of them, and determine the value of Eötvös parameter, $\hat{I}\cdot$, which measures the strength of the violation of WEP. For one case (${}^{87}$Rb$|\text{F}=1⟩$ - ${}^{85}$Rb$|\text{F}=2⟩$),the statistical uncertainty of $\hat{I}\cdot$ is $1.8\times 10^{-10}$ at integration time of 8960 s. With various systematic errors correction, the final value is $\hat{I}\cdot =(-4.4\pm 6.7)\times 10^{-10}$. Comparing with the previous WEP test experiments using atoms, this work gives a new upper limit of WEP violation for ${}^{87}$Rb and ${}^{85}$Rb atom pairs.

5 pages, 3 figures