Entanglement and decoherence in electron microscopy

Highlights: • In spite of the fundamental interest in the subject, probe-target entanglement in the electron microscope has not been discussed up to now. • Entanglement is closely related to the von Neumann entropy, a measure of the information content of an electron scattering experiment. • The relationship between entanglement, density matrices, and coherence in electron microscopy is discussed. • An experiment to measure decoherence times on the order of nanoseconds is proposed. This is especially important in view of recent developments in time resolved electron microscopy. - Abstract: Interaction of the probe with the specimen in an electron microscope inevitably leads to entanglement between the probe and the scatterer. In spite of the importance of entanglement in many areas of modern physics, this subject has not been touched in the literature. Here, we develop some ideas about entanglement in electron microscopy for a number of scattering mechanisms. The relationship between entropy, density matrices, and coherence is discussed. In addition, we explore the questions "Why is Bragg scattering coherent and energy loss incoherent?" and "When does decoherence play a role?" It seems to be possible to measure decoherence on extremely short timescales of $\sim {10}^{-8}\text{s}$. This is especially important in view of recent developments in ultrafast electron microscopy.