Experiments on ultracold atoms are enabling us to learn about the quantum mechanics of collections of particles, giving insight into phenomena which is both intellectually stimulating and possibly applicable. This award supports a theoretical study divided into three parts: (1) The researchers will engineer a system which will allow cold atom experimentalists to "mock-up" one of the most important models of high energy physics: Quantum Electrodynamics. (2) The researchers will produce new insight into a classic model of condensed matter physics: the Hoffstaedter model. (3) The researchers will study how newly accessible geometries modify one of the most exotic phenomena from semiconductor physics: the fractional quantum Hall effect. These three studies all involve "gauge fields", and are woven together by a number of intellectual threads. The intellectual merit of the first topic is that opens up a new research direction, and paves the way towards using cold atoms to study models which are relevant to high energy physics. This is a novel, and potentially transformational, direction for cold atom physics. The second topic is fundamental, and has intrigued physicists for half a century. Not only does it have intrinsic intellectual merit, but the new capabilities of cold atom systems means that this physics is now experimentally relevant. The primary intellectual merit of the third topic lies in its importance for current experiments, which naturally involve quasi- one dimensional geometries. The third topic also naturally builds on important NSF sponsored theoretical work recently completed by researchers from the condensed matter community.
This award features several broader impacts. First, much of the work will be performed by graduate students, who will learn both physics, and the tools of scientific research. Second, the principal investigator is involved in an important project aimed at addressing the national shortage of high school physics teachers. He is active in Cornell's efforts to give undergraduate physics students teaching experiences, and helping encourage them to become teachers. Third, the principal investigator is involved in more general efforts to increase the numbers of undergraduate physicists trained at Cornell, with a particular interest in diversity issues.
This was a very successful research program with 19 published peer reviewed papers, and 1 preprint which is currently under review. There were also 2 non-peer reviewed invited papers. The intellectual merit of these activites come from advancing our understanding of matter at extremely low temperatures. Our most profound results came from numerical studies of atoms trapped in periodic potentials formed from the interference pattern of laser beams. Under appropriate circumstances, one can engineer a situation where the neutral atoms in this potential act like charged particles in a magnetic field. They can undergo an interaction driven phase transition to an exotic state of matter with ``topological order". We modelled the evolution of this state when additional laser beams are dragged through it. We numerically showed that one can implement quantum computation protocols by appropriately moving these beams. Much of our studies focussed on explaining mysteries seen in experiments. For example, we helped resolve anomalously slow motion of "tidal waves" in experiments on cold Lithium atoms at MIT. We studied atomic bound states in optical lattices, and a number of exotic superfluid states. These works helped significantly advance the field, and are inspiring new experiments. Broader impact from this work came from: (1) training graduate students, (2) involvement in teacher education efforts, and (3) increasing the number of undergraduate physics majors at Cornell (and thus addressing an important need). In particular, by implementing new recruiting strategies, and streamlining the major, we were able to double the number of graduating physics majors from 2009 to 2012. Furthermore, we have increased the number of Cornell physics majors going into teaching, thus helping aleviate the national shortage of highschool physics teachers.
