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arXiv:2307.09208 · Annalen der Physik

Hong‐Ou‐Mandel Interference on a Lattice: Symmetries and Interactions

Mama Kabir Njoya Mforifoum, Andreas Buchleitner, Gabriel Dufour

Published Nov 6, 2024• 0 citations
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Abstract

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.

DOI
10.1002/andp.202400132

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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.
Tight binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. It is tempting to use the static and mobile versions of the particles to store and process information respectively. Motivated by this, we show how a beam splitter between two hopping particles traveling from distant lattice sites can be implemented by an on-site potential at the center of the lattice. We show how this enables the two mode Hong-Ou-Mandel effect to be observed, and how the intra-site interaction results in a crossover from bosonic to fermionic behavior close to the superfluid-Mott transition point. A tunable Mach-Zehnder interferometer is implemented adding a step-like potential. Finally we discuss how our results may pave the way towards the realization of a KLM quantum computer with bosonic neutral atoms in a lattice setup.
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection R=1/2R = 1/2R=1/2 and transmission $ T = 1/2 $. In this work, the general mechanism of the interaction of two photons in a beam splitter is considered using an analytical solution, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only $ R = 1/2 $ and $ T = 1/2 $, but also their root-mean-square fluctuations $ ΔR ^ 2, ΔT ^ 2 $, which arise due to the dependence of $R = R(ω_1, ω_2) $ and $ T = T (ω_1, ω_2) $ on the frequencies where ω1,ω2ω_1, ω_2ω1​,ω2​ are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations $ ΔR^2 $ and $ ΔT^2 $ can be neglected and $ R=T=1/2 $ is chosen, the developed theory coincides with previously known results.
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.
The Hong-Ou-Mandel interferometer is a foundational tool in quantum optics with both fundamental and practical significance. Earlier works identified that input-state symmetry under exchange of the two spatial modes is fundamental in the understanding of the Hong-Ou-Mandel effect. We now show that this notion of symmetry is central to generalizing this effect. In particular, this point of view enables the construction of extensions beyond the standard two single-photon case to arbitrary input states, as well as to configurations with more than two spatial modes via a natural generalization of the beam splitter to a discrete Fourier transform interferometer. Beyond its conceptual significance, this framework offers direct insights into quantum metrology, showing how symmetry properties of input states allow for the computation of explicit precision bounds. By focusing on symmetry, we provide a perspective that simplifies and unifies a range of known results while paving the way for new developments in quantum interference and sensing.
When two indistinguishable bosons interfere at a beam splitter, they exit through the same output port. This quantum effect, known as Hong-Ou-Mandel interference, underpins many protocols in quantum information. It also generalizes to larger numbers of identical particles, for which interference produces characteristic many-body patterns. So far, experiments have observed the many-particle regime mainly in photonic platforms with unavoidable loss, and atomic realizations have remained challenging. Here we demonstrate Hong-Ou-Mandel interference with up to 12 indistinguishable neutral atoms in a system with negligible loss. Single-particle counting reveals parity oscillations, a bunching envelope and genuine multipartite entanglement, which are defining features of the multiparticle Hong-Ou-Mandel effect. Using the generated quantum states, we demonstrate metrological sensitivities that scale with the number of particles according to the Heisenberg limit. Our technique can be extended to larger ensembles, with wide-ranging applications from high-precision atom interferometry to multiparticle Bell tests.