Imprinting the quantum statistics of photons on free electrons

The science of light has undergone two major revolutions over the previous two centuries. The first-by Grimaldi, Huygens, Fresnel, Young, and Maxwell-established light as a wave phenomenon, and the second-by Planck, Einstein, and Glauber-established light as a combined particle-wave quantum phenomenon. Despite the quantum revolution, entire areas of science still find the classical wave description of light sufficient, especially so for interactions between light and charged particles such as free electrons. Light and all forms of electromagnetic fields remain pure wave phenomena at the frontiers of free-electron physics, microscopy, accelerators, and radiation sources. We present experiment and theory in which the quantum nature of light plays the key role in its interaction with free electrons.