Establishing Earth's Matter Effect in Atmospheric Neutrino Oscillations at IceCube DeepCore

The discovery of the non-zero value of $\theta_{13}$ has opened an exciting opportunity to probe the Earth's matter effects in three-flavor oscillations of atmospheric neutrinos. These matter effects depend on both neutrino energy and the electron density distributions encountered during their propagation through Earth. In this contribution, we present preliminary sensitivities from the DeepCore detector, a densely instrumented sub-array of the IceCube neutrino observatory at the South Pole, demonstrating its ability to observe these matter effects in atmospheric neutrino oscillations. Using simulated data equivalent to 9.3 years of observations at IceCube DeepCore, we show the sensitivity of the DeepCore to reject the vacuum oscillation hypothesis and align with the Preliminary Reference Earth Model. Additionally, we present the expected improvement in sensitivity for rejecting the vacuum oscillations using the upcoming IceCube Upgrade, a low-energy extension of the IceCube detector.