Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models

Abstract

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 SU(N ) Hubbard models at any integer filling ρ. By calculating the ground states of one-dimensional SU(N ) Fermi-Hubbard models for 2 ≤ N ≤ 6 with use of the density matrix renormalization group method, we confirm the relation numerically in the regime of strong interactions U t, where U and t denote the onsite 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 ρ = 1 at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.