Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime

Abstract

Ultracold spinor atoms in the weak and strong interaction regimes have been extensively investigated, while the behavior in the intermediate regime is less understood. We numerically investigate one-dimensional ultracold spinor atomic ensembles of finite size in the intermediate interaction regime and reveal the evolution of the eigenstates from the strong to the intermediate regime. In the strong interaction regime, it is well known that the eigenstates can be categorized into different manifolds, and the categorization is protected by the energy gaps between manifolds. In the intermediate interaction regime, it is found that the eigenenergy spectrum becomes gapless, while categorization of the eigenstates is still preserved even without the protection from the intermanifold gaps. The categorization in the intermediate regime is found due to the minigap induced by the finite-size effect, which prevents the intermanifold coupling. The gap vanishing in the spectrum induces both direct and avoided crossings between close-lying manifolds, of which the combined symmetries determine the type of the crossings. A modified $t\text{\ensuremath{-}}J$ model is derived to describe the low-lying eigenstates in the intermediate regime, which can capture the formation and crossings of the manifolds. State preparation through avoided crossings is also investigated.