  The quantum statistics of atoms is typically observed in the behavior of an
ensemble via macroscopic observables. However, quantum statistics modifies the
behavior of even two particles, inducing remarkable consequences that are at
the heart of quantum science. Here we demonstrate near-complete control over
all the internal and external degrees of freedom of two laser-cooled 87Rb atoms
trapped in two optical tweezers. This full controllability allows us to
implement a massive-particle analog of a Hong-Ou-Mandel interferometer where
atom tunneling plays the role of a photon beamsplitter. We use the
interferometer to probe the effect of quantum statistics on the two-atom
dynamics under tunable initial conditions, chosen to adjust the degree of
atomic indistinguishability. Our work thereby establishes laser-cooled atoms in
optical tweezers as a new route to bottom-up engineering of scalable,
low-entropy quantum systems.
