  A quantum device for measuring two-body interactions, scalar magnetic fields
and rotations is proposed using a Bose--Einstein condensate (BEC) in a ring
trap. We consider an imbalanced superposition of orbital angular momentum modes
with opposite winding numbers for which a rotating minimal atomic density line
appears. We derive an analytical model relating the angular frequency of the
minimal density line rotation to the strength of the non-linear atom-atom
interactions and the difference between the populations of the
counter-propagating modes. Additionally, we propose a full experimental
protocol based on direct fluorescence imaging of the BEC that allows to measure
all the quantities involved in the analytical model and use the system for
sensing purposes.
