Competing Orders in Quantum Gases with Long-range Interactions

George Mason University, Fairfax VA

Investigators

Abstract

Recent experiments with trapped ensembles of magnetic atoms and/or polar molecules (molecules that have an electric dipole moment) have achieved the extremely cold temperatures at which quantum mechanical effects abound. Polar atoms and molecules attract and/or repel one another anisotropically (like a pair of magnets), and trapped collections of such particles are expected to display a variety of collective phenomena that are the focus of much current research. Modern experiments with dipolar gases are attempting to provide a controlled environment in which to synthesize, tune, and discover novel phases of polar quantum matter, complementary to the solid, liquid, gas and plasma phases familiar at higher temperatures. While polar systems are expected to display a wide variety of new phenomena, they are not yet well understood and their properties are challenging to predict theoretically. The difficulty arises from their sensitivity: Even small changes in density or temperature can change the phase of the ensemble, and so change observed properties dramatically. This project is developing new theoretical tools for the analysis of the plurality of phases of ultracold dipolar matter in order to improve our understanding of recent experimental observations. Graduate and undergraduate students will be trained through this project in scientific computing, data analysis and visualization in addition to physics. The project will develop two innovative many-body techniques for quantum gases with long-range interactions. The first is functional renormalization group for continuum Fermi gases at finite temperatures. It will be used to analyze the many-body instabilities and phase diagrams of dipolar Fermi gases in two-dimensions. The second is tensor network variational ansatz for dipolar atoms or molecules localized in deep optical lattices. It will be benchmarked and adapted to solve effective spin models with competing and long-range exchange interactions. The renormalization group technique will also be applied to study the many-body phases of other quantum gas systems including Rydberg dressed Fermi gases and spin-orbit coupled Fermi gases.