Testing the universality of free fall with atoms in different quantum states

We present tests of the universality of free fall by comparing the gravity acceleration of the $^{\mathrm{87}}$Rb atoms in m$_{\mathrm{F}}=$1 versus those in m$_{\mathrm{F}}=-$1, of which the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is $\eta =$(0.2\textpm 1.2) × 10$^{\mathrm{-7}}$. This also gives an upper limit of 5.4 × 10$^{\mathrm{-6}}$ m$^{\mathrm{-2}}$ for a possible gradient field of the spacetime torsion. The interferometer using atoms in m$_{\mathrm{F}}=$\textpm 1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment. Other quantum tests of the universality of free fall with atoms in magnetic-insensitive states by employing larger enclosed spacetime area atom interferometer are discussed. \textbf{References } [1] Xiao-Chun Duan, Xiao-Bing Deng, Min-Kang Zhou, Ke Zhang, Wen-Jie Xu, Feng Xiong, Yao-Yao Xu, Cheng-Gang Shao, Jun Luo, and Zhong-Kun Hu*\textbf{, }Physical Review Letters, 117, 023001(2016); [2] Min-Kang Zhou, Le-Le Chen, Qin Luo, Ke Zhang, Xiao-Chun Duan, and Zhong-Kun Hu*, Physical Review A, ~93, 053615(2016).