Comparing fractional quantum Hall Laughlin and Jain topological orders with the anyon collider

TL;DR

This study uses an anyon collider to compare topological orders in fractional quantum Hall states, demonstrating the ability to distinguish different anyon species and revealing effects of interchannel interactions.

Contribution

It introduces a method to differentiate between various topological orders and anyon species using an anyon collider in fractional quantum Hall states.

Findings

Anyon collisions on the outer channel of ν=2/5 resemble ν=1/3 behavior.

Inner channel anyons at ν=2/5 show reduced bunching, indicating different statistics.

Interchannel interactions influence anyon collision outcomes.

Abstract

Anyon collision experiments have recently demonstrated the ability to discriminate between fermionic and anyonic statistics. However, only one type of anyons associated with the simple Laughlin state at filling factor $\nu=1/3$ has been probed so far. It is now important to establish anyon collisions as quantitative probes of fractional statistics for more complex topological orders, with the ability to distinguish between different species of anyons with different statistics. In this work, we use the anyon collider to compare the Laughlin $\nu=1/3$ state, which is used as the reference state, with the more complex Jain state at $\nu=2/5$, where low energy excitations are carried by two co-propagating edge channels. We demonstrate that anyons generated on the outer channel of the $\nu=2/5$ state (with a fractional charge $e^*=e/3$) have a similar behavior compared to $\nu=1/3$, showing the robustness of anyon collision signals for anyons of the same type. In contrast, anyons emitted on the inner channel of $\nu=2/5$ (with a fractional charge $e^*=e/5$) exhibit a reduced degree of bunching compared to the $\nu=1/3$ case, demonstrating the ability of the anyon collider to discriminate not only between anyons and fermions, but also between different species of anyons associated with different topological orders of the bulk. Our experimental results for the inner channel of $\nu=2/5$ also point towards an influence of interchannel interactions in anyon collision experiments when several co-propagating edge channels are present. A quantitative understanding of these effects will be important for extensions of anyon collisions to non-abelian topological orders, where several charged and neutral modes propagate at the edge.