Fourier analysis of many-body transition amplitudes and states

TL;DR

This paper introduces a Fourier-based method to analyze many-body transition amplitudes and states, revealing how exchange symmetries influence interference patterns in quantum systems of identical particles.

Contribution

It develops a novel Fourier transform approach over the symmetric group to decompose many-body interference statistics by exchange symmetries, applicable to bosons and fermions.

Findings

Identifies mechanisms for destructive interference in many-body systems.

Provides a formalism to analyze partial distinguishability effects.

Unifies analysis of bosonic and fermionic interference patterns.

Abstract

We decompose the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. To do so, we perform a Fourier transform over the symmetric group $S_N$ on the collection of $N!$ many-body transition amplitudes connecting two states of a system of $N$ particles. We apply our formalism to the interference of partially distinguishable bosons and fermions and describe mechanisms responsible for completely destructive interference in many-body systems obeying specific exchange symmetries, including, but not limited to, bosons and fermions.