Bichromatic Tweezers for Qudit Quantum Computing in $^{87}$Sr

Neutral atoms have become a competitive platform for powering robust, scalable quantum systems for metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits composed of states spanning a large $J$ hyperfine state, compromising qudit coherence. In this paper we present a novel scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. By leveraging light shifts in $5s5p \ ^{3}\mathrm{P}_{2} \ F=9/2$, it is possible to suppress differential light shifts in this metastable state using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio. These conditions endow the bichromatic tweezer with controlled suppression of light-shift induced dephasing, enabling scalar and tensor magic conditions for qudits. Furthermore, this technique enables robust operation at the tensor magic angle 54.7$^\circ$, while further reducing sensitivity to uncertainty in experimental parameters. We expect this technique to enhance nuclear spins' coherence times, permit the implementation of new loading protocols, enhance cooling efficiency, and present a suitable regime for a qudit-based quantum computing in $^{87}$Sr.