Signatures of manyparticle interference
Abstract
Quantum systems with many constituents give rise to a range of conceptual, analytical and computational challenges, hence, the label 'complex systems'. In the first place, one can think of interactions, described by a manybody Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, manybody systems are more than just the sum of their parts. This feature is due to manybody interference. One of the most wellknown interference phenomena is the HongOuMandel effect, where total destructive interference is observed for a pair of (noninteracting) identical photons. This twophoton interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting manyparticle interference goes beyond quantum statistical effects that are contained in the BoseEinstein or FermiDirac distributions, and is dynamical in nature. 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 manyparticle interference. Its impact on manyparticle 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 manyparticle 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 manyparticle interference lead us to a statistical version of the HongOuMandel effect. The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 February 2020
 DOI:
 10.1088/13616455/ab5c30
 arXiv:
 arXiv:1908.08370
 Bibcode:
 2020JPhB...53d3001W
 Keywords:

 interference;
 identical particles;
 bosons;
 fermions;
 boson sampling;
 random matrix theory;
 distinguishability transition;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 Tutorial / Pedagogical review