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. 
Jairo Sinova, C. B. Hanna, A.H. MacDonald