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 $\rho$. By calculating the ground states of one-dimensional SU$(N)$ 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 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 $\rho =1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.

arXiv comment11 pages, 3 figures. Fixed sign error in eqs. (14,16,17,18). This error had no effect on any of the numerical results or conclusions

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