Generalized Interference of Fermions and Bosons

TL;DR

This paper develops a mathematical framework using representation theory to analyze the interference patterns of partially distinguishable fermions and bosons in interferometry, extending understanding beyond fully indistinguishable particles.

Contribution

It introduces a general expression for coincidence rates of particles with arbitrary distinguishability and applies Gamas's theorem to identify zero-contribution terms, enabling new sampling schemes like Generalized Fermion Sampling.

Findings

Derived a universal formula for particle coincidence rates with partial distinguishability.

Applied Gamas's theorem to simplify the expressions by identifying zero terms.

Proposed a novel sampling scheme for partially-distinguishable fermions.

Abstract

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of particles. In an experiment with $n$ particles the expressions we derive contain a term for each partition of the integer $n$; Gamas's theorem is used to determine which of these terms are automatically zero based on the pairwise level of distinguishability between particles. Most sampling schemes (such as Boson Sampling) are limited to completely indistinguishable particles; our work aids in the understanding of systems where an arbitrary level of distinguishability is permitted. As an application of our work we introduce a sampling scheme with partially-distinguishable fermions, which we call Generalized Fermion Sampling.