Supersolidity in Rydberg tweezer arrays

Rydberg tweezer arrays provide a versatile platform to explore quantum magnets with dipolar XY or van-der-Waals Ising ZZ interactions. Here, we propose a scheme combining dipolar and van-der-Waals interactions between two Rydberg states, where the amplitude of the latter can be greater than that of the former, realizing an extended Hubbard model with long-range tunnelings in optical tweezer arrays. On the triangular lattice with repulsive interactions, we predict the existence of a robust supersolid phase with a critical entropy per particle $S/N \approx 0.19$ accessible in current Rydberg tweezer experiments supported by large-scale quantum Monte Carlo simulations. We further demonstrate the experimental feasibility by identifying pairs of Rydberg states in ${}^{87}$Rb realizing the required interactions. Such a lattice supersolid is long-lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry, and can be realized for 100s of particles allowing one to directly probe the defect-induced picture of supersolids. Its thermodynamical and dynamical properties can hence be studied at a far larger scale than hitherto possible.