Multiphoton Interference with a symmetric SU(N) beam splitter and the generalization of the extended Hong-Ou-Mandel effect

Quantum Physics arXiv:2601.03395 (quant-ph) [Submitted on 6 Jan 2026] Title:Multiphoton Interference with a symmetric SU(N) beam splitter and the generalization of the extended Hong-Ou-Mandel effect Authors:Paul M. Alsing, Richard J. Birrittella, Peter L. Kaulfuss View a PDF of the paper titled Multiphoton Interference with a symmetric SU(N) beam splitter and the generalization of the extended Hong-Ou-Mandel effect, by Paul M. Alsing and 1 other authors View PDF HTML (experimental) Abstract:We examine multiphoton interference with a symmetric $SU(N)$ beam splitter $S_N$, an extension of features of the $SU(2)$ 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons $n/N$ in each output port), when a total number $n$ of photons impinges on the $N$-port device. These are transitions of the form $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$, where $n=\sum_{i=1}^N n_i$, which generalize the Hong-Ou-Mandel (HOM) effect $|1,1\rangle \overset{S_2}{\to}|1,1\rangle $, the eHOM effect $|n_1,n_2\rangle \overset{S_2}{\to}|\tfrac{n_1+n_2}{2},\tfrac{n_1+n_2}{2}\rangle $, and the generalized HOM effect (gHOM) $|1\rangle^{\otimes N}\overset{S_N}{\to}|1\rangle^{\otimes N}$, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of sub-amplitudes of the total zero amplitude. We develop symmetry properties for the generalized eHOM effect (geHOM) $|n_1,n_2,\ldots,n_N\rangle\overset{S_N}{\to}|n/N\rangle^{\otimes N}$ involving a zero amplitude governed by Perm($\Lambda$)=0, for an appropriately constructed matrix $\Lambda(S_N)$ built from the matrix elements of $S_N$. We develop an analytical constraint equation for Perm$(\Lambda)$ for arbitrary $N$ that allows us to determine when it is zero. We generalize the SU(2) beam splitter feature of central nodal line (CNL), which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of $N = 2 * N'$ where $N'\in odd$. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.03395 [quant-ph] (or arXiv:2601.03395v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.03395 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Paul M. Alsing [view email] [v1] Tue, 6 Jan 2026 20:16:13 UTC (2,563 KB) Full-text links: Access Paper: View a PDF of the paper titled Multiphoton Interference with a symmetric SU(N) beam splitter and the generalization of the extended Hong-Ou-Mandel effect, by Paul M. Alsing and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)