Entanglement-based 3D magnetic gradiometry with an ultracold atomic scattering halo

Ultracold collisions of Bose-Einstein condensates can be used to generate a large number of counter-propagating pairs of entangled atoms, which collectively form a thin spherical shell in momentum space, called a scattering halo. Here we generate a scattering halo initially composed of pairs in a symmetric entangled state in spin, and observe a coherent oscillation with an anti-symmetric state during their separation, due to the presence of an inhomogeneous magnetic field. We demonstrate a novel method of magnetic gradiometry based on the evolution of pairwise correlation, which is insensitive to common-mode fluctuations of the magnetic field. Furthermore, the highly multimode nature and narrow radial width of scattering halos enable a 3D reconstruction of the interrogated field. Based on this, we apply Ramsey interferometry to realise a 3D spatial reconstruction of the magnetic field without the need for a scanning probe.