Measuring the condensate fraction of rapidly rotating trapped boson systems: off-diagonal order from the density

We demonstrate a direct connection between the density profile of a system of ultra-cold 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.Comment: 4 pages, 3 figures, version accepted for publication in Phys. Rev. Let