Pathway from condensation via fragmentation to fermionization of cold bosonic systems.

For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density gradually acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes fermionized. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and coexistence of condensed and fermionized parts that are separated in space.