Strong Correlations in Cold atoms and Dirac materials

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Quantum technologies that involve the storage, transmission and manipulation of quantum information are an important direction for Canadian Physics research in the 21st Century.  Many different platforms for these technologies are currently being explored.  Two physical systems that have been suggested as possible settings for future quantum technologies are trapped cold atoms and novel electronic phases in quantum materials.  In these systems much of the most fundamentally interesting and technologically relevant novel physics is found in regimes where interactions between quantum particles are strong.  This motivates my research program, which focuses on developing theoretical techniques to study strongly interacting quantum systems, and applying these methods to specific physical systems of current interest.  Two systems I propose to investigate are i) disordered and many body localized (MBL) cold atom systems and ii) fractional quantum Hall states in graphene and generalizations of Dirac fermions. In order to manipulate quantum information it is necessary to store it - MBL systems: disordered interacting quantum systems which do not equilibrate, have been suggested as possible quantum memories.  The physics of MBL is still being established, including whether it can occur in dimensions greater than one, as suggested by recent cold atom experiments.  I have developed a theoretical  approach to the out of equilibrium dynamics of cold atoms described by the Bose Hubbard model which gives access to physics inaccessible by conventional methods. I will extend this method and apply it to the experimentally realized situation to assess claims of MBL. The integer and fractional quantum Hall (FQH) effects take place when two dimensional systems, such as graphene, are placed in strong perpendicular magnetic fields. Some FQH states have been suggested as possible candidates for fault tolerant quantum computing.  The FQH effect (FQHE) in graphene differs from the FQHE in conventional semiconductor systems due to the relativistic dispersion and internal degrees of freedom (valley and spin) of quasiparticles in graphene.  These features, in conjunction with electron interaction induced broken symmetry states, lead to a rich array of possible FQHE states in graphene which are currently not distinguished by experiment.  I will develop theory to aid discrimination between different FQHE states.  I will also explore generalizations of the Dirac fermions seen in graphene, which may allow for scenarios for materials realizations of relativistic particles that go beyond those accessible in high energy physics. The results of this research will be timely theoretical contributions to important current problems and high quality training of HQP.  Insights from these contributions may have implications for developments in quantum technologies such as quantum simulation using cold atoms, the use of MBL for quantum memories, or platforms for quantum computation.