The nonlinear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology. Yet, it poses considerable challenges to control interactions on the individual particle level. Here, we probe the coincidence correlations at a mesoscopic constriction between individual ballistic electrons in a system with unscreened Coulomb interactions and introduce concepts to quantify the associated parametric nonlinearity. The full counting statistics of joint detection allows us to explore the interaction-mediated energy exchange. We observe an increase from 50% up to 70% in coincidence counts between statistically indistinguishable on-demand sources and a correlation signature consistent with the independent tomography of the electron emission. Analytical modelling and numerical simulations underpin the consistency of the experimental results with Coulomb interactions between two electrons counterpropagating in a quadratic saddle potential. Coulomb repulsion energy and beam splitter dispersion define a figure of merit, which in this experiment is demonstrated to be sufficiently large to enable future applications, such as single-shot in-flight detection and quantum logic gates.

分束器对相互作用粒子同时到达的非线性响应使得量子工程和计量学中的众多应用成为可能。然而，它对控制单个粒子水平上的相互作用提出了相当大的挑战。在这里，我们探讨了具有未屏蔽库仑相互作用的系统中各个弹道电子之间介观收缩处的重合相关性，并引入了量化相关参数非线性的概念。联合检测的完整计数统计使我们能够探索相互作用介导的能量交换。我们观察到统计上无法区分的按需源和与电子发射的独立断层扫描一致的相关特征之间的重合计数从 50% 增加到 70%。分析模型和数值模拟巩固了实验结果与在二次鞍形电势中反向传播的两个电子之间的库仑相互作用的一致性。库仑排斥能和分束器色散定义了品质因数，在本实验中证明该品质因数足够大，足以支持未来的应用，例如单次飞行中检测和量子逻辑门。