Recent cosmogenic neutrino search results with IceCube and prospects with IceCube-Gen2

Neutrinos with energies beyond PeV (extremely high energy, EHE) are produced in interaction of the highest energy cosmic rays. One contribution to the EHE neutrino flux is expected to arise from so-called cosmogenic neutrinos generated in ultra high energy cosmic ray interactions with cosmic microwave background photons. Observation of cosmogenic neutrinos can probe the nature of cosmic rays beyond the energies for resonant photo-pion production (GZK cutoff). The IceCube detector instruments a cubic kilometer of the South Pole ice to detect Cherenkov light emitted by charged particles produced in neutrino interactions. In the future IceCube-Gen2 will increase the effective detection volume for EHE neutrinos by adding radio antennas to the in-ice detector. In this contribution we present new constraints on the EHE neutrino flux above $5 \times 10^6$ GeV using 12.6 years of IceCube data. The differential upper limit constrains the all-flavor EHE neutrino flux at 1 EeV to below a level of $E^2 \Phi \sim 10^{-8} \, \mathrm{GeV} \, \mathrm{cm}^{-2} \, \mathrm{s}^{-1} \, \mathrm{sr}^{-1}$. Additionally, we also describe the projected sensitivity of the IceCube-Gen2 radio array, which will reach fluxes about 1.5 orders of magnitude smaller than the current limits at 1 EeV.