Signatures of Many-Particle Interference

TL;DR

This tutorial explores the mathematical description of many-particle interference in quantum systems, focusing on signatures detectable through symmetry-based destructive interference and statistical correlations, including a statistical Hong-Ou-Mandel effect.

Contribution

It introduces efficient methods to observe many-particle interference signatures, overcoming computational challenges in large systems of identical particles.

Findings

Detection of fragile destructive interference in symmetric interferometers

Identification of statistical correlation signatures in output ports

Development of a statistical version of the Hong-Ou-Mandel effect

Abstract

This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on many-particle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle interference. A first type of signatures relies on the detection of a highly sensitive -but also highly fragile-processes of total destructive interference that occurs in interferometers with a high degree of symmetry. A second class of signatures is based on the statistical features that arise when we study the typical behaviour of correlations between a small number of the interferometer's output ports. We will ultimately show how these statistical signatures of many-particle interference lead us to a statistical version of the Hong-Ou-Mandel effect.