Novel Ultrafast Molecular Imaging Based on the Combination of X-ray and Electron Diffraction

Recent development of X-ray free-electron lasers and megaelectronvolt radio-frequency electron guns have made ultrafast X-ray and electron diffraction measurements possible, thereby capturing chemical dynamics with atomic-spatial and femtosecond-temporal resolutions. We present a unified formulation of standard homodyne-detected and heterodyne-detected signals for both techniques. Noting that X-rays scatter from molecular electrons while electrons scatter from both molecular electrons and nuclei, we show how the two diffraction signals can be combined to reveal novel chemical information that is unavailable by solely using each technique alone. By subtracting the homodyne-detected X-ray and electron diffraction signals, a mixed electronic-nuclear interference in electron diffraction can be identified with a self-heterodyne nature for the direct imaging of attosecond electron dynamics where the scattering off molecular nuclei serves as a local oscillator for the scattering off molecular electrons. By subtracting heterodyne-detected X-ray and electron diffraction, the purely nuclear charge density can be singled out.