Confined ultracold atoms provide the unique capability to create designer systems that can be tailored to provide direct access to quantum mechanical properties that may be otherwise obscured. An important class of such properties is topological in nature in the sense that they are primarily defined by the structure of the abstract space of their defining parameters. Since topology is the most general description of any structure, real or abstract, such features can be used to find connections among phenomena that may seem unrelated, and thereby provide powerful insights into them all. The goal of this research is to analyze several such phenomena, some newly proposed here and some well-known but not well-understood, comparatively from a topological perspective. The method will be to recast them as generalized transport problems, tracking how the system and its parameters evolve in time, which will then be related to dynamical experiments with cold atoms. The study will involve the intrinsic quantum characteristic of phase in the context of creating gauge fields associated with varying local phase, and coherence effects associated with quantum systems. Whether the topological properties survive the loss of phase coherence in the presence of nonlinearity or in taking the classical physics limit is an essential fundamental physics question that will be examined for all mechanisms studied.
The outcome of this study has potential for applications in creating novel materials and devices that take advantage of the newly available topological and phase properties, as well as, for significantly broadening our understanding of fundamental physics, since many of these issues have relevance across all areas of physics. Some aspects of the research have technological applications potential for improved sensors and gyroscopes, and in the emerging field of atomtronics, the atomic analog of electronics. A high priority of the research will be to engage multiple undergraduate students at a public university attended by many first generation and at-risk students who often do not get the opportunity to participate in scientific research. The goal is to continue and expand on the success of a prior grant to attract and channel such domestic students into careers in science and technology.
