  We present a model of a spin-squeezed rotation sensor utilising the Sagnac
effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input
states for the interferometer are seeded using Raman pulses with Laguerre-Gauss
beams and are amplified by the bosonic enhancement of spin-exchange collisions,
resulting in spin-squeezing and potential quantum enhancement in the
interferometry. The ring geometry has an advantage over separated beam path
atomic rotation sensors due to the uniform condensate density. We model the
interferometer both analytically and numerically for realistic experimental
parameters and find that significant quantum enhancement is possible, but this
enhancement is partially degraded when working in a regime with strong atomic
interactions.
