Braids and Beams: Exploring Fractional Statistics with Mesoscopic Anyon Colliders

TL;DR

The paper develops a non-equilibrium bosonization framework to analyze current cross correlations in an anyon collider, showing that the normalized correlations depend universally on the anyon exchange phase $\theta_a$ and the dynamical exponent $\delta$, enabling interferometer-free demonstrations of fractional statistics. For Laughlin states at $\nu=1/m$, with $e^*=e/m$ and $\theta_a=\pi/m$, the zero-bias cross-correlation satisfies $P(0)=1-\frac{\tan\theta_a}{\tan\pi\delta}\frac{1}{1-2\delta}$, giving $P(0)=-\frac{2}{m-2}$ at $\delta=1/m$, a prediction corroborated experimentally for $\nu=1/3$. The work extends to hierarchical states like $\nu=2/5$ by incorporating a finite soliton width $\tau_s$, which resolves ambiguities for $\theta_a>\pi/2$ and yields negative Fano factors in line with observations, through a framework where time-domain braiding governs the observed interference. Overall, the results frame a robust, transport-based approach to quantify anyonic statistics via braiding in time, consistent with ${\sf K}$-matrix edge theory and applicable to multi-mode edge structures.

Abstract

Anyon colliders -- quantum Hall devices where dilute quasiparticle beams collide at a quantum point contact -- provide an interferometer-free probe of anyonic exchange phases through current cross correlations. Within a non-equilibrium bosonization framework, the normalized cross-correlations take a universal form depending only on the exchange phase and the dynamical exponent, enabling experimental demonstration of anyonic statistics. This result can be interpreted as time-domain interference -- braiding in time rather than spatial exclusion or real-space interferometry. Extension to hierarchical states shows that the semiclassical step-function description of quasiparticles fails at large statistical angles. Introducing a finite soliton width resolves this issue and enables quantitative modeling of charge-$e/5$ quasiparticle collisions.

Figures (3)

• Figure 1: Schematic setup of an anyon collider. Dilute anyon beams are generated at QPC1 and QPC2 with small transmission probabilities $T_u$ and $T_d$, collide at QPC3, and are collected at drains D2 and D3. The resulting current cross correlations are measured at drains D2 and D3 (adapted from Ref. Ro+16.
• Figure 2: Left panel: A step of height $2\theta_a$ in the boson field $\phi$ represents the passage of a quasiparticle with exchange phase $\theta_a$. For $\theta_a>\pi/2$, the finite width $\tau_s$ of the step must be included (adapted from Ref. Thamm24). Right panel: Normalized cross-correlations [Eq. (\ref{['norm_zerobias.eq']})] versus relative bias $I_-/I_+$, for $e^*/e = \lambda=\delta=1/m$ and $\theta_a=\pi/m$. Solid line: $m=3$; dotted: $m=5$; dashed: $m=7$ (adapted from Ref. Ro+16).
• Figure 3: Time-domain interpretation of the non-equilibrium tunneling correlator $\langle A(t_0) A^\dagger(0)\rangle$. Left panel: At $t=0$, the operator $A^\dagger$ creates a low-energy qp-qh pair at the collision QPC, propagates until annihilated at $t_0$ by $A$. During the time interval $(0,t_0)$, $N_u = 2$ high-energy anyons arrive from the source QPC, each contributing a phase $e^{2i\theta_a}$. The power law factor in Eq. \ref{['quantumcorrelation.eq']} describes the quantum mechanical amplitude for the qp-qh pair not moving away from the QPC. Right panel: The qp-qh propagation from $0$ to $t_0$ forms a closed loop in time encircling the arriving anyons, corresponding to a total phase $2\theta_a$ for each anyon which passes the collision QPC.