Quantum statistics in extended collider coupled to two-level impurity

Mesoscopic colliders are a very effective platform for extracting the mutual statistics of quantum particles. More recently, in addition to electrons (fermions), mutual statistics of more exotic particles called anyons have been extracted in real experimental setups using a point-like collider called a quantum point contact. In Ref. [1], it was shown that a point-like collider coupled to a two-level impurity (a qubit) can lead to a statistical transmutation of fermions i.e., tendency to bunch together (like bosons) when compared to classical particles. Here, we extend the analysis to a collider with non-point-like geometry, recently analyzed in Ref. [2]. We analyze the physics of two incoming wave packets of fermions/bosons and write down all the possible choices of benchmarks of bunching to determine the mutual statistics. We then show that, out of all the possible benchmarks, only one successfully determines the true mutual statistics of fermions/bosons.

[1] S. Barbarino, R. Fazio, V. Vedral, and Y. Gefen, Phys. Rev. B 99, 045430 (2019)

[2] S. S. Samal, S. Vishveshwara, Y. Gefen and J. I. Vayrynen, arXiv:2412.19674 (2024)