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arXiv:2307.09222

Hong-Ou-Mandel interference of composite particles

Mama Kabir Njoya Mforifoum, Andreas Buchleitner, Gabriel Dufour

Published Jul 18, 2023• 0 citations
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Abstract

We study the Hong-Ou-Mandel interference of two identical, composite particles, each formed of two bosonic or fermionic constituents, as they scatter against a potential barrier in a one-dimensional lattice. For tightly bound composites, we show that the combination of their constituents' mutual interactions and exchange symmetry gives rise to an effective nearest-neighbour interaction between composites, which induces a reduction of the interference contrast.

DOI
10.48550/arxiv.2307.09222

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We study the Hong-Ou-Mandel interference of two identical, composite particles, each formed of two bosonic or fermionic constituents, as they scatter against a potential barrier in a one-dimensional lattice. For tightly bound composites, we show that the combination of their constituents' mutual interactions and exchange symmetry gives rise to an effective nearest-neighbour interaction between composites, which induces a reduction of the interference contrast.
Abstract The Hong‐Ou‐Mandel interference of two identical particles evolving on a 1D tight‐binding lattice where a potential barrier plays the role of a beam splitter is described. Careful consideration of the symmetries underlying the two‐particle interference effect allows to reformulate the problem in terms of ordinary wave interference in a Michelson interferometer. This approach is easily generalized to the case where the particles interact, and we compare the resulting analytical predictions for the bunching probability to numerical simulations of the two‐particle dynamics.
We investigate multi-boson interference. A Hamiltonian is presented that treats pairs of bosons as a single composite boson. This Hamiltonian allows two pairs of bosons to interact as if they were two single composite bosons. We show that this leads to the composite bosons exhibiting novel interference effects, such as Hong–Ou–Mandel interference. We then investigate generalisations of the formalism to the case of interference between two general composite bosons. Finally, we show how one can realise interference between composite bosons in the two-atom Dicke model.
The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different numbers of perfect bosons and fermions, which allows us to provide the full Hong-Ou-Mandel-like counting statistics of interfering composites. Our theory quantitatively relates the deviation from the ideal bosonic interference pattern to the entanglement of the fermions within a single composite boson.
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 many-body Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, many-body systems are more than just the sum of their parts. This feature is due to many-body interference. One of the most well-known interference phenomena is the Hong–Ou–Mandel effect, where total destructive interference is observed for a pair of (non-interacting) identical photons. This two-photon interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting many-particle interference goes beyond quantum statistical effects that are contained in the Bose–Einstein or Fermi–Dirac 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 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. The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.
In quantum mechanics, the exchange symmetry of wave functions for identical particles has observable effects, including the widely studied Hong–Ou–Mandel (HOM) effect. A theoretical description using second quantization is elegant but abstract. In contrast, this paper describes a simple model of two-particle interference using a one-dimensional delta potential well as a beam splitter. The conditions for the HOM effect are derived from the perspective of wave packet evolution. Furthermore, the interference processes of bosons, fermions, and distinguishable particles are demonstrated and compared in detail. The method presented here is concrete, easy to visualize, and can help students to better understand the effects arising from the exchange symmetry of wave functions. The main results can be animated for classroom teaching or developed into an undergraduate seminar topic.