Destructive interference and inertial noise in matter-wave interferometry

Matter-wave interferometry is highly susceptible to inertial acceleration noises arising from the vibration of the experimental apparatus. There are various methods for noise suppression. In this paper, we propose leveraging the cross-correlation of multidirectional vibration noises to mitigate their dephasing effect in matter-wave interferometers. Specifically, we analyze an interferometer driven by its internal state under an external field and examine the dephasing caused by a two-dimensional random inertial force. As we will demonstrate, the coupling between the two-dimensional inertial force noise components will shift the resonance peak but not change the shape of the power spectral density. Moreover, when the noise approximately resonates with the intrinsic frequency of the test mass, we find that the standard deviation of the phase can be suppressed by a factor roughly equal to the Q factor of the noise. This technique holds significant potential for future gravity experiments utilizing quantum sensors, such as measuring gravitational acceleration and exploring quantum entanglement induced by gravity.