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The recent high-statistics high-energy atmospheric neutrino data collected byIceCube open a new window to probe new physics scenarios that are suppressed inlower energy neutrino experiments. In this paper we analyze the IceCubeatmospheric neutrino data to constrain the Violation of Equivalence Principle(VEP) in the framework of three neutrinos with non-universal gravitationalcouplings. In this scenario the effect of VEP on neutrino oscillationprobabilities can be parametrized by two parameters $\Delta \gamma_{21}\equiv\gamma_2-\gamma_1$ and $\Delta\gamma_{31}\equiv \gamma_3-\gamma_1$, where$\gamma_i$'s denote the coupling of neutrino mass eigenstates to gravitationalfield. By analyzing the latest muon-tracks data sets of IceCube-40 andIceCube-79, besides providing the 2D allowed regions in$(\phi\Delta\gamma_{21},\phi\Delta\gamma_{31})$ plane, we obtain the upperlimits $|\phi\Delta\gamma_{21}| < 9.1\times 10^{-27}$ (at 90\% C.L.) whichimproves the previous limit by $\sim4$ orders of magnitude and$|\phi\Delta\gamma_{31}| \lesssim 6\times 10^{-27}$ (at 90\% C.L.) whichimproves the current limit by $\sim1$ order of magnitude. Also we discuss indetail and analytically the effect of VEP on neutrino oscillationprobabilities.

Constraining the Violation of Equivalence Principle with IceCube Atmospheric Neutrino Data