Fig. 1: Single-site addressing with movement-induced phase shifts.

a, We consider two atoms individually trapped in optical tweezers, both initially in the electronic ground state. Travelling light emitted from a global laser beam applies a π/2 rotation to both atoms, and is disabled, but remains phase coherent with the atomic transition. One of the atoms is then moved by half the laser wavelength (λ) from its initial position, rotating the effective local laser frame by an angle ϕ = π. When the laser drive is restarted to apply another π/2 pulse, the moved atom now rotates back to the ground state, whereas the static atom rotates to the excited state. b, Control over the atom displacement Δx is equivalent to arbitrary local rotations of the laser drive by ϕ = kΔx about the \(\hat{Z}\) axis. c, We implement this protocol with an array of ⁸⁸Sr atoms utilizing the ultranarrow ¹S₀ ↔ ³P₀ transition with λ = 698.4 nm for global driving. d, With an array of 39 tweezers in one dimension (top), we apply the protocol in b, shifting every odd site (purple markers) in the array and leaving all the even sites static (blue markers) during the dynamics. A sinusoidal oscillation emerges in the excited state population of the shifted sites (bottom), with a period of 699(1) nm. e, Focusing on the region around Δx = λ (grey-shaded region in d), we find that the shifted atom shows no measurable loss in fidelity compared with the unshifted atoms. Correcting for the bare fidelity for performing a global \(\hat{X}(\uppi )\) rotation (red dashed line; 0.9956(1)), we find that the shift operation is performed with a fidelity of 0.9984(5). The ratio of the shifted to unshifted fidelities is 0.9998(5), suggesting that the dominant source of error comes from global laser phase noise during the finite wait time required to perform the shift, rather than the movement itself. From the data in d, we find that the crosstalk to the static atoms is 0.1(2)%, consistent with 0. f, The shift to apply a \(\hat{Z}(2\uppi )\) rotation can be performed without a noticeable loss of fidelity down to shift times of ∼20 μs; the data in e are taken with a shift time of 32 μs, in addition to an extra wait time of 34 μs to account for finite jitter in the control timings.