Joint mass-and-energy test of the equivalence principle at the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:msup></mml:math> level using atoms with specified mass and internal energy
Lin Zhou, Chuan He, Sitong Yan, Xi Chen, D. Gao, Wei-Tao Duan, Yu-Hang Ji, Rundong Xu, Biao Tang, Chao Zhou, Sachin Barthwal, Qi Wang, Zhuo Hou, Zongyuan Xiong, Yuan‐Zhong Zhang, Min Liu, Wei-Tou Ni, Jin Wang, Mingsheng Zhan
Abstract
We use rubidium atoms with specified mass and internal energy to carry out a joint mass-energy test of the equivalence principle (EP). We improve the four-wave double-diffraction Raman transition method (4WDR) we proposed before to select atoms with a certain mass and angular momentum state, and form a dual-species atom interferometer. By using the extended 4WDR to $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ atoms with different angular momenta, we measure their differential gravitational acceleration, and we determine the value of the E\"otv\"os parameter, $\ensuremath{\eta}$, which measures the strength of the violation of EP. The E\"otv\"os parameters of the four paired combinations $^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}$, $^{85}\mathrm{Rb}|F=2\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}$, $^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=1\ensuremath{\rangle}$, and $^{85}\mathrm{Rb}|F=3\ensuremath{\rangle}\text{\ensuremath{-}}^{87}\mathrm{Rb}|F=2\ensuremath{\rangle}$ were measured to be ${\ensuremath{\eta}}_{1}=(1.5\ifmmode\pm\else\textpm\fi{}3.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${\ensuremath{\eta}}_{2}=(\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}3.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${\ensuremath{\eta}}_{3}=(\ensuremath{-}2.5\ifmmode\pm\else\textpm\fi{}4.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and ${\ensuremath{\eta}}_{4}=(\ensuremath{-}2.7\ifmmode\pm\else\textpm\fi{}3.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, respectively. The violation parameter of mass is constrained to ${\ensuremath{\eta}}_{0}=(\ensuremath{-}0.8\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and that of internal energy to ${\ensuremath{\eta}}_{E}=(0.0\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ per reduced energy ratio $a$ ($a=h{\ensuremath{\nu}}_{0}/{m}_{i}^{85}{c}^{2}$, and ${\ensuremath{\nu}}_{0}=1$ GHz). This work opens a door for joint tests of two attributes beyond the traditional pure mass or energy tests of EP with quantum systems.