Realizing Exotic Quantum States with Cold Atoms

Cornell University, Ithaca NY

Investigators

Abstract

Simple rules can lead to complicated behavior. This maxim is particularly true in quantum mechanics, the theory describing microscopic objects such as atoms. Tools of theoretical physics will be used to determine how such exotic behavior emerges in ultracold atomic gases. While these studies may potentially lead to novel applications in areas such as quantum computing, metrology, or materials science, the direct goal of this set of projects is to test fundamental concepts about emergent physics in quantum systems. There are three disconnected lines of research. First, when atoms are confined to tight tubes they behave differently than atoms which are free to move in three dimensions. The cross-over between this exotic one-dimensional state and more conventional three-dimensional physics will be studied. Second, an exotic state was recently discovered in electronic systems. Dubbed "topological insulators," these materials have insulating bulks, but conducting surface modes. Moreover the surface modes behave in unconventional ways. The cold atom analogs of these systems will be studied. Finally, the cold atom analogs of electron systems with magnetic impurities will be studied. Metals with magnetic impurities display a number of important phenomena, some of which are not completely understood. The goal is to produce a controlled system for testing various theoretical ideas. This project has three research directions which will advance understanding of cold atoms, and many-body physics. These are chosen to dovetail with recent experimental and theoretical development. The first research direction will involve the dimensional crossover between 1D and 3D in a superfluid partially polarized Fermi gas. The 1D system displays a fluctuating version of the FFLO state. There is hope that true long-range FFLO order can be stabilized for intermediate confinement. The PI will use the inhomogeneous Bogoliubov-de-Gennes equations to study this crossover. The second research direction will involve lattice defects in an artificial atomic Chern insulator. There is a potentially transformitive conjecture that such defects are related to the fractional quantum Hall effect. Much of this physics can be revealed by numerical studies of the single-particle Schrodinger equation. Even if the conjecture is incorrect, the study will teach us about these defects, which are important in solid state systems. The third research project will involve attempts to see Kondo physics in cold atoms. By studying this problem in cold atoms, the goal is to obtain a more direct insight into this exotic physics. Greens function techniques will be used for this latter project.