  We report constraints on nonstandard neutrino interactions (NSI) from the
observation of atmospheric neutrinos with IceCube, limiting all individual
coupling strengths from a single dataset. Furthermore, IceCube is the first
experiment to constrain flavor-violating and nonuniversal couplings
simultaneously. Hypothetical NSI are generically expected to arise due to the
exchange of a new heavy mediator particle. Neutrinos propagating in matter
scatter off fermions in the forward direction with negligible momentum
transfer. Hence the study of the matter effect on neutrinos propagating in the
Earth is sensitive to NSI independently of the energy scale of new physics. We
present constraints on NSI obtained with an all-flavor event sample of
atmospheric neutrinos based on three years of IceCube DeepCore data. The
analysis uses neutrinos arriving from all directions, with reconstructed
energies between 5.6 GeV and 100 GeV. We report constraints on the individual
NSI coupling strengths considered singly, allowing for complex phases in the
case of flavor-violating couplings. This demonstrates that IceCube is sensitive
to the full NSI flavor structure at a level competitive with limits from the
global analysis of all other experiments. In addition, we investigate a
generalized matter potential, whose overall scale and flavor structure are also
constrained.
