Partitioning of diluted anyons reveals their braiding statistics

Abstract

Correlations of partitioned particles carry essential information about their quantumness¹. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particles' charge^2,3. This is not the case when a highly diluted beam is partitioned. Bosons or fermions will exhibit particle antibunching (owing to their sparsity and discreteness)^4-6. However, when diluted anyons, such as quasiparticles in fractional quantum Hall states, are partitioned in a narrow constriction, their autocorrelation reveals an essential aspect of their quantum exchange statistics: their braiding phase⁷. Here we describe detailed measurements of weakly partitioned, highly diluted, one-dimension-like edge modes of the one-third filling fractional quantum Hall state. The measured autocorrelation agrees with our theory of braiding anyons in the time domain (instead of braiding in space); with a braiding phase of 2θ = 2π/3, without any fitting parameters. Our work offers a relatively straightforward and simple method to observe the braiding statistics of exotic anyonic states, such as non-abelian states⁸, without resorting to complex interference experiments⁹.