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

TL;DR

This paper explores the behavior of ultracold spinor atoms in the intermediate interaction regime, revealing manifold overlaps, crossings, and a modified t-J model to describe these phenomena, bridging the understanding between weak and strong interactions.

Contribution

The study introduces a detailed numerical analysis of eigenstate evolution and a modified t-J model for intermediate interactions in ultracold spinor atoms, filling a knowledge gap.

Findings

Eigenstates remain categorized with overlapping manifolds in the intermediate regime.

Energy spectrum becomes quasi-continuous with manifold overlaps and crossings.

Modified t-J model effectively describes low-lying eigenstates and crossings.

Abstract

Ultracold spinor atoms in the weak and strong interaction regime have received extensive investigations, while the behavior in the intermediate regime is less understood. We numerically investigate 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 has been well known that the low-lying eigenenergy spectrum presents the well-gaped multi-manifold structure, and the energy gaps protect the categorization of the eigenstates. In the intermediate interaction regime, it is found that the categorization of the eigenstates is preserved, and the eigenenergy spectrum become quasi-continuum, with different manifolds becoming overlapped. The overlapping induces both direct and avoided crossings between close-lying manifolds, which is determined by the combined symmetries of the eigenstates involved in the crossing. A modified t-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 the avoided crossings is also investigated.