Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based setups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be encoded in the joint probability distribution of two or more interferometers, provided that these are initialized in suitable states. We develop a general framework that makes use of $N+1$ interferometers, which may differ in their masses, to correct for environmental potential fields up to order $N$ in their multipole expansion. Remarkably, our approach works for fields that fluctuate stochastically in any timescale and does not require the presence of quantum correlations among the different interferometers. Finally, we also show that the same ideas can be extended to the protection of entanglement between pairs of interferometers.

• Received 16 August 2021
• Accepted 10 May 2022

DOI:https://doi.org/10.1103/PhysRevA.105.063313