  We use differential Ramsey interferometry of ultracold atoms to characterize
the vector light shift (VLS) from a far-off resonance optical dipole trap at
$\lambda = 1064\,\mathrm{nm}$. The VLS manifests as a `fictitious' magnetic
field, which we perceive as a change in the Larmor frequency of two spinor
condensates exposed to different intensities of elliptically polarized light.
We use our measurement scheme to diagnose the light-induced magnetic field and
suppress it to $2.1(8)\times10^{-4}$ of its maximum value, by making the
trapping light linearly polarized with a quarter-wave plate in each beam. Our
sensitive measurement of the VLS-induced field demonstrates high-precision,
in-vacuo interferometric polarimetry of dipole trapping light and can be
adapted to measure vector shifts from other lasers, advancing the application
of optically trapped atoms to precision metrology.
