 A Bose-Einstein condensate, BEC, in a ring trap is proposed as a quantum device for measuring two-body interactions, scalar magnetic fields, and rotations using an imbalanced superposition of orbital angular momentum modes with opposite winding numbers. An analytical model is derived relating the angular frequency of the minimal density line rotation to the strength of non-linear atom-atom interactions and population differences between counter-propagating modes. The system can be used for sensing purposes through direct fluorescence imaging of the BEC. This article was authored by G. Peligree, J. Mompart, and Via Hufinger.