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

## TL;DR

This paper presents a highly precise test of the weak equivalence principle using dual-species rubidium atom interferometry, achieving an upper limit of WEP violation at the 10^{-10} level.

## Contribution

The study introduces an improved four-wave double-diffraction Raman transition method for joint atom selection and conducts a dual-species interferometry test comparing different rubidium isotopes with internal energy states.

## Key findings

- Measured Eötvös parameter $\
- Final $\
- Statistical uncertainty of $1.8 imes 10^{-10}$

## 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 E\"{o}tv\"{o}s parameter, $\eta$, which measures the strength of the violation of WEP. For one case ($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statistical uncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s. With various systematic errors correction, the final value is $\eta=(-4.4 \pm 6.7) \times 10^{-10}$. 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.