Realizing anyons requires advancing the experimental state of the art. For intrinsic anyonic phases, exquisite control over microscopic interactions is required to favor topologically ordered states over the host of competing topologically trivial phases. For extrinsic anyons, gapless 1D ‘wires’ must be constructed that admit multiple gapping mechanisms—e.g., pairing and backscattering.

Our proposed efforts utilize the shared virtues of cold atoms and van der Waals heterostructures—widely tunable interactions and physical geometries—while leveraging the special advantages of each platform, namely graphene’s unique electronic structure and the ability to tune microscopic cold-atom Hamiltonians with time-dependent potentials. We will develop three experimental avenues to nonabelian physics, focusing on the most promising cold-atom and solid-state candidates: realizing intrinsic non- abelian ground states, engineering synthetic nonabelian defects via Cooper pairing, and creating nonabelian defects by purely geometric means. The mutually complementary nature of our solid- state and cold-atom approaches is an advantage of this approach. As an example, cold atoms straightforwardly realize disorder-free systems but often suffer from relatively high temperatures, while solid-state systems can be easily cooled but preclude total control over sample disorder.

Even as we advance both fields through innovations in atomic cooling and fabrication of ultra-clean heterostructures, our joint effort will provide ample opportunity for reciprocal quantum emulation: atomic systems can simulate anyonic signatures in disordered solid-state systems using tunable disorder, while finite-temperature effects can be controllably simulated in solid-state systems. In many cases, our proposed platforms admit new probes that have never been applied to anyonic systems, including spatially resolved transport, thermodynamics, and spectroscopic measurements – facilitating an unprecedented characterization of nonabelian anyons not possible in either setting by itself.