It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of $\mathrm{SU}\left(N\right)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional $\mathrm{SU}\left(N\right)$ Fermi-Hubbard models for $2\le N\le 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U\gg t$, where $U$ and $t$ denote the on-site interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately ${(t/U)}^2$ for $\rho =1$ at intermediate and large lattice sizes on the basis of numeric and semianalytic arguments.

• Received 24 January 2023
• Accepted 27 March 2023
• Corrected 7 December 2023

DOI:https://doi.org/10.1103/PhysRevA.107.043313