We apply the notion of discrete supersymmetry based on matrix factorization to quantum systems consisting of coupled bosonic oscillators to construct isospectral bosonic quantum networks. By using the algebra that arises due to the indistinguishability of bosonic particles, we write down the Schrodinger equations for these oscillators in the different boson-number sectors. By doing so, we obtain, for every partner quantum network, a system of coupled differential equations that can be emulated by classical light propagation in optical waveguide arrays. This mathematical scheme allows us to build quasi-two-dimensional optical arrays that are either isospectral or share only a subset of their spectrum after deliberately omitting some chosen eigenstates from the spectrum. As an example, we use this technique (which we call bosonic discrete supersymmetry or BD-SUSY) to design two optical, silica-based waveguide arrays consisting of six and three elements, respectively, with overlapping eigenspectrum.

中文翻译：

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准二维光学阵列的玻色子离散超对称性

我们将基于矩阵分解的离散超对称概念应用于由耦合玻色子振荡器组成的量子系统，以构建等谱玻色子量子网络。通过使用由于玻色子粒子的不可区分性而产生的代数，我们写下了这些振荡器在不同玻色数扇区中的薛定谔方程。通过这样做，我们为每个合作伙伴量子网络获得了一个耦合微分方程系统，可以通过光波导阵列中的经典光传播来模拟。这种数学方案允许我们构建准二维光学阵列，这些阵列要么是等谱的，要么在故意从光谱中省略一些选定的本征态后仅共享其光谱的一个子集。举个例子，