  Current optical atomic clocks do not utilize their resources optimally. In
particular, an exponential gain in sensitivity could be achieved if multiple
atomic ensembles were to be controlled or read-out individually, even without
entanglement. However, controlling optical transitions locally remains an
outstanding challenge for neutral atom based clocks and quantum computing
platforms. Here we show arbitrary, single-site addressing for an optical
transition via sub-wavelength controlled moves of tweezer-trapped atoms, which
we perform with $99.84(5)\%$ fidelity and with $0.1(2)\%$ crosstalk to
non-addressed atoms. The scheme is highly robust as it relies only on relative
position changes of tweezers and requires no additional addressing beams. Using
this technique, we implement single-shot, dual-quadrature readout of Ramsey
interferometry using two atomic ensembles simultaneously, and show an
enhancement of the usable interrogation time at a given phase-slip error
probability. Finally, we program a sequence which performs local dynamical
decoupling during Ramsey evolution to evolve three ensembles with variable
phase sensitivities, a key ingredient of optimal clock interrogation. Our
results demonstrate the potential of fully programmable quantum optical clocks
even without entanglement and could be combined with metrologically useful
entangled states in the future.
