Quantum sensing using imbalanced counter-rotating Bose-Einstein condensate modes

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 nonlinear 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.