Characterization of a Simultaneous Dual-Species Atom Interferometer for a Quantum Test of the Weak Equivalence Principle

We present here the performance of a simultaneous dual-species matter-wave accelerometer for measuring the differential acceleration between two different atomic species ($^{87}$Rb and $^{85}$Rb). We study the expression and the extraction of the differential phase from the interferometer output. The differential accelerometer reaches a short-term sensitivity of $1.23\times10^{-7}g/\sqrt{Hz}$ limited by the detection noise and a resolution of $2\times10^{-9}g$ after 11000 s, the highest reported thus far with a dual-species atom interferometer to our knowledge. Thanks to the simultaneous measurement, such resolution levels can still be achieved even with vibration levels up to $3\times10^{-3}g$, corresponding to a common-mode vibration noise rejection ratio of 94 dB (rejection factor of 50 000). These results prove the ability of such atom sensors for realizing a quantum based test of the weak equivalence principle (WEP) at a level of $\eta\sim10^{-9}$ even with high vibration levels and a compact sensor.