  Many-body interference between indistinguishable particles can give rise to
strong correlations rooted in quantum statistics. We study such Hanbury
Brown-Twiss-type correlations for number states of ultracold massive fermions.
Using deterministically prepared $^6$Li atoms in optical tweezers, we measure
momentum correlations using a single-atom sensitive time-of-flight imaging
scheme. The experiment combines on-demand state preparation of highly
indistinguishable particles with high-fidelity detection, giving access to two-
and three-body correlations in fields of fixed fermionic particle number. We
find that pairs of atoms interfere with a contrast close to 80%. We show that
second-order density correlations arise from contributions from all
two-particle pairs and detect intrinsic third-order correlations.
