This proposal describes a theoretical study of the rotational properties of clouds of ultracold atoms. Building on his previous work, the investigator will explore several topical subjects, with the fol- lowing four objectives. (1) He will calculate the topological structures which will form in a rapidly rotating gases of spin-1 bosons in the presence of magnetic fields. (2) He will determine the kinet- ics of spinning up small clusters of atoms at the nodes of an optical lattice. (3) He will produce a practical scheme for creating fields which couple to neutral atoms in the same way that the electromagnetic fields couple to charged particle. (4) He will study interference between rotating clouds and demonstrate that an interference experiment can distinguishing condensed and strongly correlated rotating states. These projects are motivated by both interest in fundamental physical properties of these cold gases [topics (1), (2), and (4)] and by a desire to produce experimental protocols to create and measure exotic states of matter [topics (2), (3), and (4)]. Topic (1) addresses the basic ground state properties of clouds of rotating atoms. Topic (2) allows the study of fundamental questions of energy and entropy transfer in isolated systems, while possibly providing an experimental pathway to producing analogs of quantum Hall effects. Topic (3) is aimed at producing a valuable tool for exploring vortex physics, quantum Hall effects, the pinning of vortex lattices, and the interplay between lattices and quantum Hall effects. Topic (4) studies the basic coherence properties of both condensed and correlated states, and provides an experimental strategy for distinguishing these states. The investigator will use an array of analytic and computational techniques, related to those used in previous projects. These include lowest-Landau-level calculus, field theory, variational methods, numerical exact diagonalization, and numerical Monte-Carlo.
