  Identification and understanding of the evolution of interference patterns in
two-particle momentum correlations as a function of the strength of interatomic
interactions are important in explorations of the nature of quantum states of
trapped particles. Together with the analysis of two-particle spatial
correlations, they offer the prospect of uncovering fundamental symmetries and
structure of correlated many-body states, as well as opening vistas into
potential control and utilization of correlated quantum states as quantum
information resources. With the use of the second-order density matrix
constructed via exact diagonalization of the microscopic Hamiltonian, and an
analytic Hubbard-type model, we explore here the systematic evolution of
characteristic interference patterns in the two-body momentum and spatial
correlation maps of two entangled ultracold fermionic atoms in a double well,
for the entire attractive- and repulsive-interaction range. We uncover
statistics-governed bunching and antibunching, as well as interaction-dependent
interference patterns, in the ground and excited states, and interpret our
results in light of the Hong-Ou-Mandel interference physics, widely exploited
in photon indistinguishability testing and quantum information science.
