The past decade has witnessed a quantum revolution in the field of computation, communication and materials investigation. A similar revolution is also occurring for free-electron based techniques, where the classical treatment of a free electron as a point particle is being surpassed toward a deeper exploitation of its quantum nature. Adopting familiar concepts from quantum optics, several groups have demonstrated temporal and spatial shaping of a free-electron wave function, developing theoretical descriptions of light-modulated states, as well as predicting and confirming fascinating phenomena as attosecond self-compression and orbital angular momentum transfer from light to electrons. In this review, we revisit the milestones of this development and the several methods adopted for imprinting a time-varying phase modulation on an electron wave function using properly synthesized ultrafast light fields, making the electron an exquisitely selective probe of out-of-equilibrium phenomena in individual atomic/nanoscale systems. We discuss both longitudinal and transverse phase manipulation of free-electrons, where coherent quantized exchanges of energy, linear momentum and orbital angular momentum mediating the electron–light coupling are key in determining their spatio-temporal redistribution. Spatio-temporal phase shaping of matter waves provides new routes toward image-resolution enhancement, selective probing, dynamic control of materials, new quantum information methods, and exploration of electronic motions and nuclear phenomena. Emerging as a new field, electron wave function shaping allows adopting familiar quantum optics concepts in composite-particle experiments and paves the way for atomic, ionic and nuclear wave function engineering with perspective applications in atomic interferometry and direct control of nuclear processes.

过去十年见证了计算、通信和材料研究领域的量子革命。基于自由电子的技术也正在发生类似的革命，其中将自由电子视为点粒子的经典处理方法正在被超越，以更深入地利用其量子性质。采用量子光学中熟悉的概念，几个小组已经证明了自由电子波函数的时间和空间成形，发展了光调制态的理论描述，以及预测和证实了阿秒自压缩和轨道角动量转移等令人着迷的现象从光到电子。在这篇综述中，我们重新审视了这一发展的里程碑，以及使用正确合成的超快光场在电子波函数上印记时变相位调制所采用的几种方法，使电子成为非平衡现象的精确选择性探针在单个原子/纳米级系统中。我们讨论了自由电子的纵向和横向相位操纵，其中介导电子-光耦合的能量、线性动量和轨道角动量的相干量子化交换是确定其时空重新分布的关键。物质波的时空相位整形为图像分辨率增强、选择性探测、材料动态控制、新的量子信息方法以及电子运动和核现象的探索提供了新途径。作为一个新兴领域，电子波函数整形允许在复合粒子实验中采用熟悉的量子光学概念，并为原子、离子和核波函数工程在原子干涉测量和核过程直接控制中的应用前景铺平道路。