CAREER: Quantum Many Body Physics in Ultracold Atomic and Molecular Gases

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An integrated approach to research and education on the frontiers of quantum mechanics is proposed. The research portion focuses on quantum many body theory and computation in ultracold gases; the educational portion focuses on reforming the advanced undergraduate and graduate curriculum, beginning with quantum mechanics, in accord with the extensive ongoing efforts at improvement in physics education at the Colorado School of Mines.Experiments on ultracold quantum gases are having a huge impact on physics and applied mathematics, particularly in atomic, molecular, and optical physics, in condensed matter theory, and in nonlinear dynamics. These gases can be trapped in lattices of arbitrary structure, all parameters are dynamically and precisely controllable, and the experiments are 100% impurity free. Thus they constitute a designer condensed matter system, with the added advantage that the microscopic parameters are extremely well known in comparison to typical solid state systems. The theory of ultracold fermionic atoms is an especially important, rapidly expanding, interdisciplinary field of study. Three principal topics of research are proposed: quantum phases and the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover; rotating lattices and otherexotic lattice configurations and phases; and quantum many body solitons and vortices. Pure and applied aspects of each topic are addressed. For instance, it is proposed to find the complete phase diagram of a multi-band Fermi-Bose Hubbard Hamiltonian with coherent conversion between Fermi-pairs and bosons, which models ultracold fermions trapped in a lattice potential of arbitrary dimension. In the educational aspect of this proposal, a thorough effort at research-based reform of quantum mechanics education is outlined. This will be done in collaboration with Noah Finkelstein and Carl Wieman in the physics education research group at the University of Colorado. Recent spectaculardevelopments in quantum mechanics, including the concepts of entanglement, decoherence, and quantum information, will be incorporated. Quantum mechanics physics demonstrations in the form of computer simulations, as part of the Physics Education Technology Project, will be developed and used, as well as improved teaching techniques, such as problem solving in the classroom.