Observation of Heterodyne Mixing in Surface X-Ray Photon Correlation Spectroscopy Experiments

We report measurements of propagating capillary waves on a liquid water surface at $T=5\text{ }\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ with x-ray photon correlation spectroscopy. The experiment has been performed under grazing incidence conditions with an incoming x-ray beam below the critical angle of total external reflection. In the $\mathbf{q}$ region investigated the measured intensity-intensity autocorrelation functions of the liquid water surface were found to be heterodyne signals, i.e., a combination of first- and second-order correlation functions ${g}_{1}(\ensuremath{\tau})$ and ${g}_{2}(\ensuremath{\tau})$.