The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with single particles and more slits produce interference fringes reducible to a combination of double-slit patterns, it is usually argued that quantum interference occurs between pairs of trajectories, compactly denoted as second-order interference. Here we show that quantum mechanics in fact allows for interference of arbitrarily high order. This occurs naturally when one considers multiple quantum objects interacting in the presence of a nonlinearity, both of which are required to observe higher-order interference. We make this clear by treating a generalized multislit interferometer using second quantization. We then present explicit experimentally relevant examples both with photons interacting in nonlinear media and an interfering Bose-Einstein condensate with particle-particle interactions. These examples are all perfectly described by quantum theory, and yet exhibit higher-order interference based on multiple particles interacting nonlinearly.

中文翻译：

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多个非线性相互作用的量子粒子之间的高阶干涉

双缝实验是单个量子物体之间干涉的最直接证明。由于对单个粒子和更多缝隙进行的类似实验产生的干涉条纹可简化为双缝隙图案的组合，因此通常认为量子干涉发生在轨迹对之间，紧凑地表示为二阶干涉。在这里，我们证明了量子力学实际上允许任意高阶的干涉。当人们认为多个量子物体在存在非线性的情况下相互作用时，自然会发生这种情况，这两个条件都需要观察到更高阶的干扰。我们通过使用第二量化处理广义多缝干涉仪来明确这一点。然后，我们提出了与光子在非线性介质中相互作用以及具有干扰性的玻色-爱因斯坦凝聚物与颗粒-颗粒相互作用的明确的实验相关示例。这些示例均已通过量子理论完美描述，但由于多个粒子非线性相互作用而显示出更高阶的干涉。