Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

TL;DR

This paper investigates how partially distinguishable bosons interfere in multi-mode networks, linking their scattering probabilities to multidimensional permanents and introducing a measure for their degree of indistinguishability.

Contribution

It introduces a tensor-permanent framework for partially distinguishable bosons and identifies the permanent of the distinguishability matrix as a key measure of interference.

Findings

The scattering probability is a multidimensional tensor-permanent.

The permanent of the distinguishability matrix quantifies interference degree.

Provides bounds on probability differences based on distinguishability.

Abstract

The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.