  We demonstrate the ability to extract a spin-entangled state of two neutral
atoms via postselection based on a measurement of their spatial configuration.
Typically, entangled states of neutral atoms are engineered via atom-atom
interactions. In contrast, in our work we use Hong-Ou-Mandel interference to
postselect a spin-singlet state after overlapping two atoms in distinct spin
states on an effective beam splitter. We verify the presence of entanglement
and determine a bound on the postselected fidelity of a spin-singlet state of
$\left(0.62 \pm 0.03\right)$. The experiment has direct analogy to creating
polarization entanglement with single photons and hence demonstrates the
potential to use protocols developed for photons to create complex quantum
states with noninteracting atoms.
