Search for non-Abelian quantal phases and statistics

Quantum statistics and the spin and symmetry of wavefunctions are central to a quantum mechanical understanding of the world. Since the dawn of quantum mechanics it has been known that statistics distinguishes fermions from bosons due to symmetry with respect to interchange of two identical particles. In three spatial dimensions there are only two possible symmetries: the wave function of bosons is symmetric under permutation of particles while for fermions the wavefunction is antisymmetric. Two-dimensional systems are qualitatively different and the wavefunction can acquire any phase factor owing to interchange of two quasiparticles. These anyonic quasiparticles obey fractional statistics and arise in the context of the fractional quantum Hall effect. Yet more exotic phases and statistics has been envisioned, in which quasiparticle states are degenerate and their state vectors are multiplied by a unitary matrix rather than a phase factor as a result of quasiparticle interchange. In such a non-Abelian many-body systems exchange of two particles changes the state of all the particles in the condensate. Such rigidity of the wavefunction has lead to the idea of a fault-tolerant quantum computer with qubits based on non-Abelian states.While theoretically non-Abelian statistics and non-Abelian quantal phases have been predicted in many systems, no experiment to date has confirmed the existence of states with non-Abelian statistics. The most promising candidate - the filling factor v = 5/2 quantum Hall state is yet to be shown to be a non-Abelian state. Unlike the non-Abelian statistics, the non-Abelian quantal phase can already be a property of a single-particle wavefunction. We propose to explore the non-Abelian quantal phase in two-dimensional hole gases with total angular momentum J = 3/2 heavy hole states. The envisaged experiments on coupled quantum rings promise to show non- Abelian many-body effects and lead to the discovery of this elusive new state of matter. The proposed research involves advanced material growth, nanofabrication, rf investigation of small energy scales and a deep understanding of holes interactions. The Semiconductor Physics group at the Cavendish Laboratory, Cambridge University, headed by Professor David Ritchie, is one of a few places in the word where such an ambitious goal of detecting non-Abelian phases can be achieved. The group pioneered the key enabling technologies, such as MBE growth of high quality two dimensional gases and low temperature rf techniques. Prof. Leonid Rokhinson from Purdue University, USA, will bring expertise of many years of investigation of holes in GaAs, development of heterostructures especially tailored for nanofabrication techniques, and recently developed strain control techniques.