Non-Abelian Phases in the Fractional Quantum Hall Regime

The fractional quantum Hall effect (FQHE) occurs in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field at low temperature. It is now understood to arise from strong electron-electron interactions. In transport experiments the FHQE is characterized by Hall resistance quantized to rational fractional values of h/e2 and vanishingly small longitudinal resistance. Quasi-particle excitations in the FQHE are called anyons. This is because anyons are neither fermions nor bosons, but rather acquire a phase upon particle exchange. In certain exotic FQHE states (e.g. ν=5/2 and ν=12/5) the excitations are theorized to be even more bizarre. Excitations for these states are believed to obey non-Abelian braiding statistics; repeated exchange of two particles does not simply induce a phase but rather results in a unitary transformation of the wavefunction within a degenerate manifold. The topology of such states potentially makes them immune to local perturbations and may allow for the construction of topologically protected qubits. Topologically protected qubits may be less susceptible to decoherence, a problem that plagues most solid-state approaches to quantum computing.

While theoretically exciting, we still don’t know much about the n=5/2 and 12/5 states including whether they do in fact support non-Abelian excitations. This is because both states are very fragile and easily disturbed by disorder. The 5/2 and 12/5 states are only seen in the highest quality samples. We have recently demonstrated GaAs 2DEGs that display exceptionally robust states at 5/2 and 12/5. Our group and our collaborators use these samples to study basic physical phenomena and test their utility as a platform for topological quantum computing.