Steve Simon

Abstract:

Anisotropic charge transport is observed in a two-dimensional (2D) hole system in a perpendicular magnetic field at filling factors nu=7/2, nu=11/2, and nu=13/2 at low temperature. In stark contrast, the transport at nu=9/2 is isotropic for all temperatures. Isotropic hole transport at nu=7/2 is restored for sufficiently low 2D densities or an asymmetric confining potential. The density and symmetry dependences of the observed anisotropies suggest that strong spin-orbit coupling in the hole system contributes to the unusual transport behavior.

Abstract:

In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected interelectron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions and for understanding the quantum Hall states that result. In the current paper, we consider the analog of this pseudopotential construction that results from general M -body interactions rather than the usual (Coulomb) two-body interaction. © 2007 The American Physical Society.

Abstract:

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm. © 2007 The American Physical Society.