This award supports theoretical research and education at the interface of theoretical condensed matter physics and atomic physics. Advances in physics come from mutual stimulation of theory and experiments. In the field of ultracold atoms theoretical ideas about Feshbach resonances, optical lattices, and low dimensional systems lead to experimental realization of several types of strongly correlated many body systems. Future progress in the field requires theoretical input into developing new methods for creation, manipulation, identification, and characterization of novel quantum states of matter realized with cold atoms. One of the goals of this research is to develop new theoretical tools for studying coherent dynamics of strongly correlated quantum systems. Understanding non-equilibrium dynamics of interacting many-body systems is crucial for making contact with experiments on ensembles of cold atoms. Theoretical techniques will include perturbative expansions, analysis of effective field theories, application of exact solutions, numerical methods for lattice systems. This project will adopt a strategy of considering particular systems with a goal of developing general tools for studying dynamics of interacting fermionic and bosonic systems and bringing out a common framework for understanding the physics of strongly correlated states of matter. Another goal of this project is to find new ways of characterizing non-trivial correlations of interacting many body systems using experimental techniques appropriate for cold atoms ensembles. Novel approaches to examining the data, such as quantum noise analysis of the time of flight experiments and analysis of fringe visibility in interference experiments will be emphasized. The theoretical investigation of new methods for creating strongly correlated systems is also an essential part of this project. This project will explore a variety of possibilities starting from non mean field states of spinor condensates and polar molecules in optical lattices to a Tonks gas of photons in a hollow optical fiber. The idea of the latter is to create a one dimensional system of photons where optical non-linearity is so large that photons become essentially impenetrable particles. Such a system should exhibit features of photon "fermionization" including the appearance of strong photon antibunching and crystal like correlations. It should provide a new intriguing interface between nonlinear quantum optics and strongly correlated electron systems. Another component of this project involves exploring new methods for studying strongly correlated states of electrons in solids using recent progress in a variety of experimental techniques, including resonant soft x-ray scattering, double photoemission spectroscopy, and high resolution scanning tunneling microscopy. Training students and postdoctoral researchers is a vital component of this project. Students and postdocs are actively involved in the research of the PI and are exposed to a wide range of problems in several areas of physics.
NON-TECHNICAL SUMMARY: This award supports theoretical research and education at the interface of theoretical condensed matter physics and atomic physics. This research project focuses on new states of matter that arise in systems of atoms trapped by light, and in low-energy electrons in complex materials. In these systems and materials, the atoms or the electrons interact strongly with each other resulting in the emergence of new states of matter with intriguing properties that often display fundamentally new phenomena. Advanced tools of theoretical research will be brought to bear to understand possible new states of matter and propose new ways to experimentally probe these systems and to manipulate their quantum mechanical states so as to identify new states of matter and discover their subtle nature. The study of cold atoms trapped in periodic lattices of light offer the possibility to explore strongly interacting systems in ways that are not possible for electrons in materials. Advances in understanding one area enable advances in the other. The unusual properties of new states of matter however they are manifest and the unusual phenomena associated with them are of no less fundamental interest and importance than any other aspect of our universe. Understanding how to manipulate newly discovered quantum mechanical states of matter offers the possibility of powerful new ways to perform computation and new device technologies that will help keep America competitive. Training students and postdoctoral researchers is a vital component of this project. Students and postdocs are actively involved in the research and are exposed to a wide range of problems in several areas of physics. This project contributes to the high caliber scientifically trained workforce of the next generation.