Spatially defined Rabi spectroscopy for uninterrupted optical clock interrogation.

Optical lattice clocks achieve fractional frequency uncertainties of 10⁻¹⁸, yet stability is constrained by the dead time between cooling, preparation, interrogation, and detection. This sampling aliases local-oscillator noise into the clock signal (the Dick effect) and prevents continuous accumulation of oscillator phase information. We demonstrate spatially defined Rabi spectroscopy of ultracold ⁸⁸Sr atoms continuously transported in a moving optical lattice. A longitudinal excitation geometry preserves Lamb-Dicke confinement and suppresses Doppler broadening. Clock excitation is enabled only within a localised region by a transverse magnetic mixing field, defining the atom-laser interaction in space rather than in time and decoupling interrogation from preparation and detection. Transporting atoms at 16 mm s⁻¹ through a 12-mm interaction region yields a 1.2-Hz-wide spectrum close to the transit-time Fourier limit while maintaining uninterrupted atom delivery. This approach provides a practical route toward dead-time-free optical clock interrogation of continuously delivered atomic ensembles.