This experimental research program extends the idea of quantum simulation to investigations of many-body Fermi systems governed by the Dirac equation. The systems studied will include up to three flavors of fermions and two additional pseudo-spin degrees of freedom. Problems germane to relativistic particle physics and nanoelectronic devices such as graphene and carbon nanotubes will be investigated. To realize a system described by the Dirac equation, fermionic Li-6 atoms will be confined in a three dimensional optical lattice with a honeycomb structure in two-dimensions. For a honeycomb lattice at half-filling (the situation realized in intrinsic graphene), low-energy excitations have a linear dispersion relation and can be formally described by a massless Dirac equation where the speed of light c is replaced by the Fermi velocity vF . The pseudo-spin degree of freedom corresponding to the four-component Dirac spinor is associated with the two interleaving triangular sub-lattices A and B which comprise the honeycomb lattice. A method for adding an adjustable mass term in the Dirac equation by producing an inequality between the A and B sublattices will be implemented.
The investigations of transport (including the role that interactions play) and mechanisms for opening a bandgap in a two-dimensional honeycomb lattice will aid in the development of nanoelectronic devices based on graphene such as ultra-high speed transistors and novel electron optics devices. Study of Klein tunneling and the opening of a bandgap due to interactions will respectively provide insight into fundamental questions regarding the electrical breakdown of the QED vacuum and chiral symmetry breaking and mass generation in QCD. Furthermore, the observation of a color superconducting phase will guide our understanding of the state of high-density nuclear matter. In carrying out this research, undergraduate students, graduate students and postdoctoral researchers will be trained in the use of modern technology, analytical thinking, scientific writing and giving clear oral presentations. This research program will continue to recruit students from demographic groups underrepresented in the sciences.
