  Ultracold collisions of Bose-Einstein condensates can be used to generate a
large number of counterpropagating pairs of entangled atoms, which collectively
form a thin spherical shell in momentum space, called a scattering halo. Here
we generate a scattering halo composed almost entirely of pairs in a symmetric
entangled state and observe a scattering angle-dependent mixing to the
anti-symmetric state due to the presence of an inhomogeneous magnetic field. We
report on a proof-of-principle application of the observed parity dynamics to
demonstrate magnetic gradiometry, insensitive to common-mode fluctuations of
the background magnetic field. Furthermore, the highly multimode nature and
narrow radial width of the scattering halos enable 3D tomography of an
interrogated field without the need for a scanning probe.

Quantum Physics