Optical intensity interferometry lab tests in preparation of stellar diameter measurements at IACTs at GHz photon rates

Astronomical intensity interferometry enables quantitative measurements of the source geometry by measuring the photon fluxes in individual telescopes and correlating them, rather than correlating the electromagnetic waves' amplitudes. This simplifies realization of large telescope baselines and high angular resolutions. Imaging Atmospheric Cherenkov Telescopes (IACTs), intended to detect the optical emission of $\gamma$-ray induced air showers, are excellent candidates to perform intensity correlations in the optical at reasonable signal-to-noise ratios. The detected coherence time is on the scale of $10^{-12}$ to $10^{-15}$~seconds - depending on the optical bandwidth of the measurement - which challenges the detection system to work in a stable and accurate way. We developed an intensity interferometry setup applicable to IACTs, which measures the photo currents from photomultipliers and correlates them offline, and as such is designed to handle the very large photon rates provided by the telescopes. We present measurements in the lab simulating starlight using a xenon lamp and measured at different degrees of temporal and spatial coherence. Necessary calibration procedures are described with the goal of understanding the measurements quantitatively. Measured coherence times between $5\,$femtoseconds (corresponding signal-to-background ratio $5\cdot10^{-7}$) and $110\,$femtoseconds (signal-to-background ratio $10^{-5}$) are in good agreement with expectations, and so are the noise levels in the correlations, reaching down to $6 \cdot 10^{-8}$, after measurements between $30\,$minutes and $1\,$ hour.