Extended Data Fig. 2: Comparison between experimental methods with and without non-reciprocal attenuator at half-filling.
From: A neutral-atom Hubbard quantum simulator in the cryogenic regime

Left to right: averages of two-dimensional singlon density, radially averaged singlon density on A/B sublattices, nearest neighbor spin correlation Czz(1) for intra-dimer, inter-dimer and perpendicular bonds, spin correlations averaged over an ROI of r = 5. The sharp edge in the spatial singlon density profile is due to the edge of the camera sensor. (a)-(d). Without the non-reciprocal attenuator, we ramp the interference time phase to ϕ = π/2 to remove the tunneling dimerization. At half-filling, the resulting sublattice potential offset would not induce a density offset in the Mott insulator region but would cause offsets away from half-filling. The density offset is clearly visible in the outer reservoir region. (e)-(h). With the non-reciprocal attenuator, we could keep the interference phase at ϕ = 0. This suppresses tunneling dimerization below statistical fluctuations without inducing sublattice potential offsets. We find no difference between the densities on the two sublattices. No density modulation is detected in the reservoir.