We report on the first observation of Bragg scattering of an ultracold $^6$Li Fermi gas. We demonstrate a Ramsey-type matter-wave interferometer based on Bragg diffraction and find robust signatures of persistent matter wave coherences using an echo pulse sequence. Because of the Pauli principle, the diffracted fermions oscillate nearly unperturbed in the trapping potential for long times beyond 2 s. This suggests extremely long coherence times. On these timescales, only the presence of a $^{87}$Rb cloud seems sufficient to induce noticeable perturbations.
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