Fractional statistics in anyon collisions (2006.13157v1)

Abstract: Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor $\nu=1/m$ (where m is an odd integer) have been predicted to obey abelian fractional statistics, with a phase $\varphi$ associated with the exchange of two particles equal to $\pi/m$. However, despite numerous experimental attempts, clear signatures of fractional statistics remain elusive. Here we experimentally demonstrate abelian fractional statistics at filling factor $\nu=1/3$ by measuring the current correlations resulting from the collision between anyons at a beam-splitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract $\varphi=\pi/3$, in agreement with predictions.

• The paper provides empirical evidence for fractional anyon statistics through measured phase shifts in quasiparticle collisions at ν=1/3.
• The authors employ quantum interferometry with quantum point contacts to analyze current cross-correlations, revealing a generalized Fano factor of -2.1 ± 0.1.
• The findings validate theoretical predictions and pave the way for exploring anyons in topological quantum computing applications.

Fractional Statistics in Anyon Collisions

The paper presented investigates the fractional statistics of anyons, specifically focusing on the conditions under which these particles manifest in two-dimensional systems subject to the fractional quantum Hall effect (FQHE). Anyons, exhibiting statistic phases that diverge from traditional bosonic or fermionic behaviors, are central to understanding two-dimensional topological states. This paper provides empirical evidence for anyonic statistics by examining quasiparticle collisions at the fractional quantum Hall effect filling factor $\nu=1/3$.

Framework and Methodology

The investigation centers around the fractional quantum Hall regime, specifically at a Landau level filling factor $\nu=1/3$. At this filling, anyons are predicted to obey Abelian fractional statistics with a phase $\varphi = \pi/3$. The authors employ a sophisticated setup involving multiple quantum point contacts (QPCs) to partition and collide anyons, utilizing conductance measurements through quantum interferometry to infer statistical phases.

The experiment utilizes a two-dimensional electron gas within a GaAs/AlGaAs heterostructure at high magnetic fields. Electrons propagating along edge channels are partitioned using QPCs, generating current fluctuations and correlations that reveal underlying quantum statistics. The central methodology involves measurements of these cross-correlation noises as fractional charges collide at a beam-splitter interface using a collider geometry, a technique beneficial for probing quantum particle statistics.

Results and Analysis

The experiments show that at $\nu=1/3$, the cross-correlations between current fluctuations deviate from those predicted by fermionic statistics, showing a negative value $P = -2.1 \pm 0.1$ as the generalized Fano factor. Notably, this result is in stark contrast to the fermionic case (where $\nu=2$) yielding $P \approx 0$. The implications of such a result confirm the expected anyonic exchange phase, $\varphi = \pi/3$, matching theoretical predictions for the Laughlin state at this filling factor.

By varying the transmissions of input QPCs and the bias voltages, the paper thoroughly explores the transition between anyonic and fermionic regimes, affirming that such a fractional behavior is contingent on maintaining a weak-backscattering condition. This consistency and coherence with theoretical predictions underscore the validity of the experimental approach.

Implications and Future Directions

The notable agreement of experimental outcomes with theoretical predictions concerning anyons has profound implications for quantum computing and condensed matter physics. Anyons, especially those with non-Abelian statistics, are proposed as candidates for topological quantum computing due to their resistance to decoherence, making them some of the most promising qubits.

Future research could extend these methodologies to explore more complex states with non-Abelian statistics, benefiting from the capacity to precisely control and measure quasiparticle interactions. Moreover, developing a more integrated approach combining triggered emission with collision experiments might allow direct manipulation and observation of anyon braiding operations, a key requirement for topological quantum computation.

In summary, this paper provides compelling experimental evidence for fractional statistics corresponding to the predicted anyonic exchange phase at fractional quantum Hall scenarios. It solidifies the operational mechanisms underlying quasiparticle behavior in two-dimensional electron systems and sets the stage for further groundbreaking research exploring the applications of anyons in quantum technologies.