  We consider a two-component Bose-Einstein condensate (BEC) in a ring trap in
a rotating frame, and show how to determine the response of such a
configuration to being in a rotating frame, via accumulation of a Sagnac phase.
This may be accomplished either through population oscillations, or the motion
of spatial density fringes. We explicitly include the effect of interactions
via a mean-field description, and study the fidelity of the dynamics relative
to an ideal configuration.

Quantum Gases