Constraining Sterile Neutrinos with AMANDA and IceCube Atmospheric Neutrino Data

We demonstrate that atmospheric neutrino data accumulated with the AMANDA and the partially deployed IceCube experiments constrain the allowed parameter space for a hypothesized fourth sterile neutrino beyond the reach of a combined analysis of all other experiments. We also illustrate the sensitivity of the completed IceCube detector, that is now taking data, to the parameter space of 3+1 model.