Quantum Gases in Quantum Hall Regime and in Spin-Orbit Coupled Regime

Ohio State University, The, Columbus OH

Investigators

Abstract

NONTECHNICAL SUMMARY The Division of Materials Research and the Physics Division contribute funds to this award. It supports theoretical research and education to study two novel phenomena in a system of atoms which are trapped by light and are very close to the absolute zero of temperature. These phenomena, the quantum Hall effect and spin-orbit coupling effects, were first discovered in a two dimensional liquid of electrons trapped in an artificial semiconductor structure in a perpendicular magnetic field and in the spectrum of light emitted by atoms. The electrons in Quantum Hall states may organize themselves in a remarkable way enabling the possibility of performing computing operations by manipulating quantum mechanical states, known as topological quantum computing. Electrons have an intrinsic property called spin where it appears as if the electron spins like a tiny top. The spin of the electron is also connected to its intrinsic magnetic properties; it behaves as though it was a tiny bar magnet. As an electron moves around the nucleus of an atom or through a solid the theory of relativity says that it will experience a magnetic field from the atomic cores in the lattice. The interaction of the electron with this magnetic field gives rise to the spin-orbit interaction. Much like the quantum Hall effect, the spin-orbit interaction in some materials gives rise to perfectly conducting states on the surfaces and edges of the material. Unlike common copper wires, these metallic states can carry currents without dissipation. This holds promise for new low-energy electronic device technologies. To create such devices requires the control to create the right effective quantum-Hall state in a spin-orbit coupled material, which is very challenging. Ultra-cold atom systems have the potential to meet this challenge because interactions can be tuned on the fly in real experiments. So, ultra-cold atoms offer a new platform for studying these novel phenomena. The research supported by this award focuses on finding new ways to realize quantum Hall states and novel spin-orbit states, but in systems composed of ultra-cold atoms instead of electrons. In the case of quantum Hall systems, the P.I. aims to first create a quantum Hall state and then to exploit the physics of cold atom systems to "bind" cold atoms together making bosons to create long sought bosonic quantum Hall states. Electrons and many atoms are fermions. In contrast to fermions, more than one boson can occupy the same quantum state. Strong electrostatic repulsion between electrons makes this process difficult in electrons in artificial semiconductiong materials and other solids, but it is possible in neutral atoms. This offers a new way to construct a wide range of quantum Hall states that have no analog in materials. This award also funds projects that study interaction effects on spin-orbit coupled systems. The goal is to understand how interactions affect the properties of these system, and to understand the mechanisms for creating new states of matter. In addition to producing systems that have analogs in solid-state systems, the research supported by this award will also study new quantum states of very high spin particles that have no solid-state analogs. Electrons are fermions that have two "spin" components. Even with just two varieties, electrons are able to produce the immense diversity of condensed matter phenomena in this world. In the case of cold atoms, there are many fermions and bosons with very high spins, some of them, like Dysprosium, have spins five times that of an electron. The condensed matter of ultra-cold large spin atoms opens a new frontier rich with new phenomena. These projects will provide training for students and postdocs in a wide range of theoretical techniques, and will help them develop expertise in cold atom and condensed matter physics, superfluid physics, and quantum Hall phenomena. TECHNICAL SUMMARY The Division of Materials Research and the Physics Division contribute funds to this award, which supports theoretical research and education to investigate new states of quantum matter that are unique to dilute quantum gases of atoms and are at the same time of fundamental significance in condensed matter. The research focuses on two areas: Quantum Hall states and large spin particles. It will address the longstanding issue of how to achieve quantum Hall states in cold gases, and will explore the novel physics of high spin bosons and fermions. There are five projects: 1. Creating bosonic quantum Hall states from filled fermionic Landau levels; 2. Realizing quantum Hall states with synthetic gauge fields; 3. Investigating spin-orbit effects in strongly repulsive 1D Fermi gases; 4. Creating synthetic gauge fields for large spin particles; 5.Exploring novel Quantum Hall states of large spin atoms. Some of these projects are in collaboration with experimental groups. The research will help realize fermionic and bosonic quantum Hall states in cold atoms, including those with non-abelian statistics that are crucial for topological quantum computation. Some of the states to be studied in this project have been predicted for an electron gas but have never been confirmed; while others such as those for large-spin particles are distinctly new states that have no electronic analogs. The study of spin-orbit effects in strongly repulsive Fermi gases will help uncover new phenomena arising from the interplay between strong interaction and spin-orbit coupling, an important area that has so far been little studied. These projects will provide training for students and postdocs in a wide range of theoretical techniques, and will help them develop expertise in cold atom and condensed matter physics, superfluid physics, and quantum Hall phenomena.