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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, |ψ⟩=12√(|gg⟩+i|ee⟩), with a fidelity of 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 τbc=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. 

Experiments and numerical simulations are described that develop quantitative understanding of atomic motion near the surfaces of nanoscopic photonic crystal waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice into the PCW. Synchronous with the moving lattice, transmission spectra for a guided-mode probe field are recorded as functions of lattice transport time and frequency detuning of the probe beam. By way of measurements such as these, we have been able to validate quantitatively our numerical simulations, which are based upon detailed understanding of atomic trajectories that pass around and through nanoscopic regions of the PCW under the influence of optical and surface forces. The resolution for mapping atomic motion is roughly 50 nm in space and 100 ns in time. By introducing auxiliary guided-mode (GM) fields that provide spatially varying AC Stark shifts, we have, to some degree, begun to control atomic trajectories, such as to enhance the flux into the central vacuum gap of the PCW at predetermined times and with known AC Stark shifts. Applications of these capabilities include enabling high fractional filling of optical trap sites within PCWs, calibration of optical fields within PCWs, and utilization of the time-dependent, optically dense atomic medium for novel nonlinear optical experiments.