We conduct the first study of the T-odd correlations in ttbar events produced in ppbar collision at the Fermilab Tevatron collider that can be used to search for CP violation. We select events which have lepton+jets final states to idenfiy tt events and measure counting asymmetries of several physics observables. Based on the result, we search the top quark anomalous couplings at the production vertex at the Tevatron. In addition, Geant4 development, photon identification, the discrimination of a single photon and a photon doublet from π⁰ decay are discussed in this thesis.