The atomic nucleus is composed of two different kinds of fermions, protons and neutrons. If the protons and neutrons did not interact, the Pauli exclusion principle would force the majority fermions (usually neutrons) to have a higher average momentum. Our high-energy electron scattering measurements using 12C, 27Al, 56Fe and 208Pb targets show that, even in heavy neutron-rich nuclei, short-range interactions between the fermions form correlated high-momentum neutron-proton pairs. Thus, in neutron-rich nuclei, protons have a greater probability than neutrons to have momentum greater than the Fermi momentum. This finding has implications ranging from nuclear few body systems to neutron stars and may also be observable experimentally in two-spin state, ultra-cold atomic gas systems.