AMANDA observations constrain the ultrahigh energy neutrino flux

A number of experimental techniques are currently being deployed in an effort to make the first detection of ultrahigh energy cosmic neutrinos. To accomplish this goal, techniques using radio and acoustic detectors are being developed, which are optimally designed for studying neutrinos with energies in the PeV-EeV range and above. Data from the AMANDA experiment, in contrast, have been used to place limits on the cosmic neutrino flux at less extreme energies (up to similar to 10 PeV). In this Letter, we show that by adopting a different analysis strategy, optimized for much higher energy neutrinos, the same AMANDA data can be used to place a limit competitive with radio techniques at EeV energies. We also discuss the sensitivity of the IceCube experiment, in various stages of deployment, to ultrahigh energy neutrinos.