Formation of spatial shell structures in the superfluid to Mott   insulator transition
  We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory. 
Simon Foelling, Artur Widera, Torben Mueller, Fabrice Gerbier and   Immanuel Bloch