Quantum statistics and self-interference in extended colliders

Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on point-like colliders, when it comes to experiment, the colliders are rarely point-like objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single or multi-particle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator which reveals the true mutual statistics of fermions.

💡 Research Summary

The paper investigates how quantum statistics manifest in “extended” colliders—devices that are not ideal point contacts but rather have a finite spatial extent, often containing resonant levels or multiple tunneling points. The authors focus on a paradigmatic fermionic collider realized with quantum Hall edge channels coupled to a circular quantum anti‑dot (QAD). Particles injected from two sources (S₁, S₂) can tunnel into the QAD, wind around it an arbitrary number of times, and then exit toward two detectors (D₁, D₂). Each tunnel junction is described by a scattering matrix with transmission amplitude t = √(1−r²) and reflection amplitude r (phase θ).

A key observation is that, because the QAD allows an infinite set of winding trajectories, a single particle’s wave packet is split into an infinite series of “wavelets” separated by the QAD circumference L. The degree of interference between different windings is controlled by the ratio of the wave‑packet width ℓ to L. In the limit ℓ ≪ L the windings do not interfere (classical limit); for ℓ ≫ L they interfere fully.

The authors first compute single‑particle transmission and reflection probabilities. In the weak‑tunneling regime (t ≪ 1) and neglecting interference, the classical probabilities are P₍Cl₎(1→2) ≈ t²/2 and P₍Cl₎(1→1) ≈ 1−t²/2. Including self‑interference modifies the transmission probability to P₍F₎(1→2) = (t²/2)