Interferometric schemes for the detection of non-abelian statistics

States of matter are conventionally classified according to broken symmetries. Topologically ordered phases fall outside of this paradigm: with no local order parameter, they nevertheless have many peculiar properties setting them apart from disordered phases. In 2D, such phases may support anyons - quasiparticles that are neither bosons nor fermions. Moreover, anyons with \emph{non-Abelian} statistics can occur, particularly in the fractional quantum Hall regime.\\ In this talk, I will focus on solid state interferometers designed to detect such exotic statistics. I will discuss recent experiments in the $\nu=5/2$ quantum Hall state where the evidence for the existence of non-Abelian quasiparticles may have in fact been observed for the first time [1]. Potential applications of such interferometeric schemes for topological quantum computation will also be addressed.\\ {[1]} R.~L.~Willett, L.~N.~Pfeiffer and K.~W.~West, PNAS \textbf{106}, 8853 (2009).