arXiv 2601.033952026-01-06quant-ph

多光子干涉与对称的SU(N)光束分裂器及扩展Hong-Ou-Mandel效应的一般化

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

Paul M. Alsing, Richard J. Birrittella, Peter L. Kaulfuss

备注：: 31 pages including 2 source code, and10 figures

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AI总结：

本文研究了对称SU(N)光束分裂器的多光子干涉，扩展了Hong-Ou-Mandel效应，并探讨了其在不同N情况下的应用。

摘要：

我们研究了使用对称的SU(N)光束分裂器S_N的多光子干涉，这是SU(2)50/50光束分裂器扩展Hong-Ou-Mandel（eHOM）效应的扩展。当总光子数n照射到N端口设备时，输出同时态态的振幅（概率）为零，该态由每个输出端口相等数量的光子n/N定义。这些是形式为|n₁,n₂,…,n_N⟩通过S_N转变为|n/N⟩⊗N的转变，其中n=∑_{i=1}^N n_i，这扩展了Hong-Ou-Mandel（HOM）效应|1,1⟩通过S₂转变为|1,1⟩，扩展HOM效应|n₁,n₂⟩通过S₂转变为|（n₁+n₂）/2,（n₁+n₂）/2⟩，以及广义HOM效应（gHOM）|1⟩⊗N通过S_N转变为|1⟩⊗N，这些之前已经在文献中研究过。本工作的重点是阐明整体破坏性干涉如何在单独的破坏性干涉子振幅组中发生。我们开发了涉及由矩阵元素构成的矩阵Λ(S_N)构建的广义扩展HOM效应（geHOM）的对称性属性，该效应由Perm(Λ)=0控制。我们开发了一个分析约束方程用于Perm(Λ)对于任意N，允许我们确定何时为零。我们扩展了SU(2)光束分裂器的中心节点线（CNL）特征，该特征在其中一个输入态为奇数奇数（只包含奇数个光子）时，输出概率分布的对角线为零，扩展到一般情况N=2*N'，其中N'为奇数。

英文摘要：

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($Λ$)=0, for an appropriately constructed matrix $Λ(S_N)$ built from the matrix elements of $S_N$. We develop an analytical constraint equation for Perm$(Λ)$ 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 $N'\in odd$.

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