Strongly Interacting and Topologically Ordered Atomic Gases

New methods to manipulate neutral atoms at ultralow temperatures permit quantum mechanical many-body phenomena to be probed in previously unimaginable ways. By precisely controlling external and interatomic potentials, new thermodynamic systems may be proactively engineered to broaden our understanding of quantum statistical mechanics and quantum field theories, and as inspiration in the search for new materials and emergent many-body phenomena. This research agenda represents a broad attempt to classify the behavior of two-dimensional quantum gases of ultracold atoms exhibiting strongly interacting behavior and topological ordering. First steps include experimental extraction of universal thermodynamic equations of state for both Bose and Fermi gases in two dimensions with resonant interactions, serving as a touchstone for understanding basic phenomena in strongly interacting two-dimensional gases. Subsequent addition of gauge potentials to both systems will facilitate a search for and characterization of topological ordering. In the case of Bosons, this expands on prior efforts in rapidly rotating clusters of particles simulating a bosonic variant of the fractional quantum Hall effect. New steps will be taken to enhance the role of interactions through Feshbach resonance, and introduce new probes using in-situ microscopy and matter-wave collapse and revival. Finally, first attempts will be made to generate controlled excitations in Bosonic fractional quantum Hall states using trapped impurity atoms. For Fermions, macroscopic numbers of particles will be placed in an optical lattice with a controlled and non-trivial topological character to simulate the intrinsic quantum anomalous Hall effect. A topological phase transition will be induced by controlling the strength of an effective gauge potential created by a time-dependent modulation of the optical lattice. The effects of this transition on the in-situ density of a trapped sample will be probed with optical microscopy.The emergence of topological ordering in many-body systems represents a fascinating convergence in interdisciplinary research. The topic draws interest from communities as diverse as pure mathematics, where the characterization of different types of order draws heavily on new concepts in topology, to computer science, where new prospects to robustly store and process quantum information arise from the manipulation of excitations of topologically ordered phases. This program will also include a strong educational component. Research will include direct mentoring of students at the undergraduate, graduate and postdoctoral level in all aspects of experimental atomic physics. The analytic and technical skills developed during this research program will facilitate new careers in both academia and industry. In addition, many of the technical aspects of this study have potential commercial and interdisciplinary academic impact.