Signature of paraparticles: a minimal Gedankenexperiment

TL;DR

This paper proposes a minimal Gedankenexperiment to detect permutation-group paraparticles, translating complex mathematical signatures into a practical flowchart for laboratory implementation, advancing experimental quantum physics.

Contribution

It introduces a simplified, theoretical test setup for detecting permutation-group paraparticles, guiding experimental realization through a logical flowchart.

Findings

The minimal setup maps paraparticle detection to a chirality test.

Mathematical framework based on $Z_2\times Z_2$-graded color Lie superalgebras.

Provides a practical guide for experimentalists to realize paraparticle detection.

Abstract

Paraparticles beyond bosons and fermions can be exchanged via either the braid group (anyons, existing up to $D=2$ space dimensions) or the permutation group; in the latter case the space dimensions are not limited. Besides being predicted, anyons have been experimentally detected. The situation differs for paraparticles exchanged via the permutation group ("permutation-group parastatistics").The first test to detect their theoretical signature was published in 2021 (for $Z_2\times Z_2$-graded parafermions; it was soon followed by a second paper proving the detectability of $Z_2\times Z_2$-graded parabosons). Later on, two further papers proved theoretical signatures of permutation-group parastatistics. These works demonstrate that, in certain situations, a long-held belief on the "conventionality of parastatistics" argument can be evaded: some measurements of permutation-group paraparticles cannot be recovered from ordinary bosons/fermions. The main question now is how to experimentally detect or engineer in the laboratory such paraparticles. For this aim a minimal setup for the theoretical test is here provided: a Gedankenexperiment (a simplified version of the two tests published in 2021) which, essentially, is a flow chart of logical operations. The key point is to present, to experimentalists, the necessary steps to be simulated/realized in the laboratory (possibly, by manipulating qudits). In this minimal setup, the detection/engineering of paraparticles is mapped into a chirality test. The mathematical setting is based on $Z_2\times Z_2$-graded color Lie (super)algebras and derived mathematical structures.