2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/19005We propose a simple scheme of generating rotating atomic clusters in an optical lattices which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increases, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum $L^{\ast}$ substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reflects the quantum Hall and the spin structure of a single cluster.4 pages, 2 figures, revtex3, psfrag; Revised May 7, 2002 -- version accepted by PRLCondensed Mattertext