Atom diffraction in the strong-coupling regime
Analytic methods based on matter-wave diffraction are a cornerstone in condensed-matter research, providing access to static and dynamic materials properties down to the atomic level. In these experiments, the shape of the diffraction pattern is largely determined by the lattice at equilibrium whereas vibrationally-induced distortions are treated perturbatively. Here, we show that the perturbative approach does not hold for helium diffracted at kiloelectronvolt energy through freestanding single-layer graphene. In this case, we enter a new regime of strong coupling where the projectile strongly interacts with the electron density of several lattice atoms simultaneously, leading to phase shifts of several radians. In consequence, lattice distortions introduce a significant phase spread that cannot be described by the typically employed Debye-Waller factor. We show that the weak-coupling regime is retained for atomic hydrogen diffraction. The experimental results are supported by simulations, providing a regime-independent approach to describe the influence of phonons on atom diffraction phenomena.