Upper limits on the amplitude of ultra-high-frequency gravitational waves from graviton-photon mixing

In this work, we present the first experimental upper limits on the presence of stochastic ultra-high-frequency gravitational waves. We exclude gravitational waves in the frequency bands from $(2.7 - 14)times10^{14}~$Hz and $(5 - 12)times10^{18}~$Hz down to a characteristic amplitude of $h_c^{rm min}approx6times 10^{-26}$ and $h_c^{rm min}approx 5times 10^{-28}$ at $95~$% confidence level, respectively. To obtain these results, we used data from existing facilities that have been constructed and operated with the aim of detecting WISPs (Weakly Interacting Slim Particles), pointing out that these facilities are also sensitive to gravitational waves by graviton to photon conversion in the presence of a magnetic field. The principle applies to all experiments of this kind, with prospects of constraining (or detecting), for example, gravitational waves from light primordial black hole evaporation in the early universe.