Experimental Determination of the $D1$ Magic Wavelength for $^{40}$K

TL;DR

This paper experimentally determines the D1 magic wavelength for fermionic $^{40}$K at 1227.54 nm, enabling improved cooling and detection in quantum simulation with neutral-atom arrays.

Contribution

First experimental measurement of the $^{40}$K D1 magic wavelength, validated by all-order calculations, facilitating high-fidelity quantum operations.

Findings

Magic wavelength for $^{40}$K D1 transition found at 1227.54 nm.

Differential AC Stark shifts mapped and matched with theoretical predictions.

Identified intensity-sampling issues at standard trapping wavelengths, mitigated at the magic wavelength.

Abstract

Neutral-atom arrays offer a promising path for quantum simulation, yet the potential of fermionic $^{40}$K remains largely constrained by state-dependent light shifts that degrade cooling and detection fidelities. This problem can be resolved by working at a magic wavelength, where the differential light shift vanishes. We report the first experimental determination of the magic wavelength for the D1 transition in fermionic $^{40}$K at 1227.54(3) nm. Using in-trap loss spectroscopy in a wavelength-tunable optical tweezer, we map the differential AC Stark shift across a range of trapping powers and wavelengths. By converting these shifts to differential scalar polarizabilities, we find excellent agreement with relativistic all-order calculations. Benchmark measurements at 1064.49 nm further reveal the significant intensity-sampling systematics that plague standard trapping wavelengths, contrasting with the "mechanically clean" environment provided by the magic condition. Our results provide an important step toward high-fidelity in-trap D1 cooling, fluorescence imaging, and light-assisted loading, establishing a robust path toward scaling fermionic neutral-atom arrays for quantum information science.