Universal nomogram for the atomtronic quantum rotation sensor

Bose-Einstein condensates in annular geometries have received significant attention due to their potential use as interferometers for inertial sensing and other applications. We systematically study the critical velocity of a barrier for vortex formation in such a geometry. More significantly, we are able to show that the details of the critical velocity can be captured by a simple analytic solution which can be considered the atomtronic analog of the usual nomographic equations for electronic circuit components. Experimentally useful nomograms can be plotted from the main result of this paper, from the analytic expression abbreviated as $\mathrm{\ensuremath{\Delta}}$, whose accuracy has been validated via full simulations. It is a function of the potential parameters only and it can be used to directly determine parameter regimes for a given application.