Proposed Experiments to Probe the Non-Abelian $\nu =5/2$ Quantum Hall State

We propose several experiments to test the non-Abelian nature of quasiparticles in the fractional quantum Hall state at $\nu =5/2$. In a simplified version of the experiment suggested by [S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005).], interference is turned on and off when the number of localized quasiparticles between the interfering paths varies between even and odd. We find analogous effects in the thermodynamic properties of closed systems.

Figure 1

Experimental setup for measuring the interference contribution to the backscattered current. Current flows along the lower edge, heading rightwards, and is backscattered by two quantum point contacts. The “island” is defined by the two quantum point contacts and the two edges. The antidot at the center of the island is coupled to an air-bridge gate that controls the number of $e/4$-charged quasiparticles that it localizes. A voltage $V_S$ applied to a side gate varies the size of the island.