  The generation of long-lived entanglement on an optical clock transition is a
key requirement to unlocking the promise of quantum metrology. Arrays of
neutral atoms constitute a capable quantum platform for accessing such physics,
where Rydberg-based interactions may generate entanglement between individually
controlled and resolved atoms. To this end, we leverage the programmable state
preparation afforded by optical tweezers along with the efficient strong
confinement of a 3d optical lattice to prepare an ensemble of strontium atom
pairs in their motional ground state. We engineer global single-qubit gates on
the optical clock transition and two-qubit entangling gates via adiabatic
Rydberg dressing, enabling the generation of Bell states, $|\psi\rangle =
\frac{1}{\sqrt{2}}\left(|gg\rangle + i|ee\rangle \right)$, with a fidelity of
$\mathcal{F}= 92.8(2.0)$%. For use in quantum metrology, it is furthermore
critical that the resulting entanglement be long lived; we find that the
coherence of the Bell state has a lifetime of $\tau_{bc} = 4.2(6)$ s via parity
correlations and simultaneous comparisons between entangled and unentangled
ensembles. Such Bell states can be useful for enhancing metrological stability
and bandwidth. Further rearrangement of hundreds of atoms into arbitrary
configurations using optical tweezers will enable implementation of many-qubit
gates and cluster state generation, as well as explorations of the transverse
field Ising model and Hubbard models with entangled or finite-range-interacting
tunnellers.
