de-Broglie Wavelength Enhanced Weak Equivalence Principle Test for Atoms in Different Hyperfine States

We report a hyperfine-states related weak equivalence principle (WEP) test which searches for possible WEP violation signal in single atom interferometer. With the ground hyperfine states $\left|F=1\right\rangle$ and $\left|F=2\right\rangle$ of $^{87}$Rb atoms simultaneously scanned over different paths in a Raman Mach-Zehnder interferometer (MZI), the difference of the free fall accelerations for the atom in the two hyperfine states is encoded into the phase shift of the MZI, contributing a WEP test signal. The test signal can be extracted out by reversing the direction of the effective wave vector of the Raman laser to suppress direction-dependent disturbances. More importantly, de-Broglie wavelength of cold atoms can be utilized to enhance the test signal in our scheme, which helps to improve the upper bound of the WEP test for atoms in different hyperfine states to $2.9\times10^{-11}$, about one order of magnitude lower than the previous record.