Measuring the Condensate Fraction of Rapidly Rotating Trapped Boson Systems: Off-Diagonal Order from the Density Profile

We demonstrate a direct connection between the density profile of a system of ultracold trapped bosonic particles in the rapid-rotation limit and its condensate fraction. This connection can be used to probe the crossover from condensed vortex-lattice states to uncondensed quantum-fluid states that occurs in rapidly rotating boson systems as the particle density decreases or the rotation frequency increases. We illustrate our proposal with a series of examples, including ones based on models of realistic finite trap systems, and comment on its application to freely expanding boson density profile measurements.