Monitoring spontaneous charge-density fluctuations by single-molecule diffraction of quantum light

Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space |σ(q)| ² , missing its phase, which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals σ(q) itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two-dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.