Quantum entangled states can exhibit nonlocal correlations that are incompatible with classical notions of causality and determinism, manifested by the violation of Bell inequalities.
So far, demonstrations of quantum nonlocality have been mostly restricted to entanglement between internal properties of systems, such as the polarisation of photons.

The environmental isolation and excellent controllability of ultracold atoms make them a favourable platform for investigating macroscopic and motional entanglement, which may be able to test theories of gravitational decoherence.

In this work, we demonstrate quantum nonlocality with freely propagating atoms, as in the original proposition of the Einstein-Podolski-Rosen paradox.

The entangled atom pairs are generated in a collision of Bose-Einstein condensates, which collectively form a thin spherical halo in momentum space, and dephase over time due to inhomogeneity in the magnetic field.
We use this fact to perform entanglement-based magnetic gradiometry.
The multimodal nature and narrow width of scattering halos enable microscopic 3D field tomography without the need for a scanning probe.
This method is intrinsically insensitive to common-mode fluctuations of the background field and, in principle, Heisenberg-limited.