The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in random matrix theory and quantum chaos for decades. Here we present an experimental observation of the lowest non-trivial Riemann zeros by using a trapped-ion qubit in a Paul trap, periodically driven with microwave fields. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function. Scanning over the driving amplitude thus enables the locations of the Riemann zeros to be measured experimentally to a high degree of accuracy, providing a physical embodiment of these fascinating mathematical objects in the quantum realm.

黎曼 zeta 函数的非平凡零点是数论的核心对象。特别是，它们使人们能够重现质数。几十年来，它们也引起了研究随机矩阵理论和量子混沌的物理学家的注意。在这里，我们通过在保罗陷阱中使用俘获离子量子位来展示最低非平凡黎曼零点的实验观察，定期用微波场驱动。驱动的波形被设计成当驱动参数与 zeta 函数的实分量的零一致时，离子的动力学被冻结。因此，扫描驱动振幅可以通过实验以高精度测量黎曼零点的位置，从而提供了量子领域中这些迷人数学对象的物理体现。