Common-mode noise rejection using fringe-locking method in WEP test by simultaneous dual-species atom interferometers

We theoretically investigate the application of the fringe-locking method (FLM) in the dual-species quantum test of the weak equivalence principle (WEP). With the FLM, the measurement is performed invariably at the midfringe, and the extraction of the phase shift for atom interferometers is linearized. For the simultaneous interferometers, this linearization enables a good common-mode rejection of vibration noise, which is usually the main limit for high precision WEP tests of the dual-species kind. We note that this method also allows for an unbiased determination of the gravity accelerations difference, which meanwhile is ready to be implemented.