The principle of least action is arguably the most fundamental principle in physics as it can be used to derive the equations of motion in various branches of physics. However, this principle has not been experimentally demonstrated at the quantum level because the propagators for Feynman’s path integrals have never been observed. The propagator is a fundamental concept and contains various significant properties of a quantum system in the path integral formulation, so its experimental observation is itself essential in quantum mechanics. Here we theoretically propose and experimentally observe the propagators of single photons based on the method of directly measuring quantum wave functions. Furthermore, we obtain the classical trajectories of single photons in free space and in a harmonic trap based on the extremum of the observed propagators, thereby experimentally demonstrating the quantum principle of least action. Our work paves the way for experimentally exploring the fundamental problems of quantum theory in the formulation of path integrals.

最小作用原理可以说是物理学中最基本的原理，因为它可以用来推导物理学各个分支的运动方程。然而，这一原理尚未在量子水平上通过实验证明，因为费曼路径积分的传播子从未被观察到。传播子是一个基本概念，在路径积分公式中包含了量子系统的各种重要性质，因此它的实验观察本身在量子力学中是必不可少的。在这里，我们基于直接测量量子波函数的方法，从理论上提出并通过实验观察单光子的传播子。此外，我们根据观察到的传播子的极值获得了自由空间和谐波陷阱中单个光子的经典轨迹，从而通过实验证明最小作用的量子原理。我们的工作为通过实验探索路径积分公式中量子理论的基本问题铺平了道路。