Ordered structures in rotating ultracold Bose gases

The characterization of small samples of cold bosonic atoms in rotating microtraps has recently attracted increasing interest due to the possibility to deal with a few number of particles per site in optical lattices. We analyze the evolution of ground state structures as the rotational frequency $\mathrm{\Omega }$ increases. Various kinds of ordered structures are observed. For $N<10$ atoms, the standard scenario, valid for large sytems, is absent, and only gradually recovered as $N$ increases. The vortex contribution to the total angular momentum $L$ as a function of $\mathrm{\Omega }$ ceases to be an increasing function of $\mathrm{\Omega }$, as observed in experiments of Chevy {\it et al.} (Phys. Rev. Lett. 85, 2223 (2000)). Instead, for small $N$, it exhibits a sequence of peaks showing wide minima at the values of $\mathrm{\Omega }$, where no vortices appear.