Density distributions for trapped one-dimensional spinor gases

TL;DR

This paper numerically investigates the density distributions of a one-dimensional spin-1 bosonic condensate in its ground state, revealing distinct behaviors under ferromagnetic and anti-ferromagnetic interactions, especially in the Tonks-Girardeau regime.

Contribution

It combines exact solutions of an integrable model with local density approximation to analyze density distributions in spinor gases, highlighting the suppression of certain spin components and Fermi-like distributions in the TG regime.

Findings

Atoms in m_F=0 state are suppressed under anti-ferromagnetic interactions.

All three spin components coexist under ferromagnetic interactions.

Fermi-like distribution emerges in the Tonks-Girardeau regime.

Abstract

We numerically evaluate the density distribution of a spin-1 bosonic condensate in its ground state within a modifed Gross-Pitaevskii theory, which is obtained by the combination of the exact solution of the corresponding integrable model with the local density approximation. Our study reveals that atoms in the m_F = 0 state are almost completely suppressed for the anti-ferromagnetic interactions in both weakly and strongly interacting regimes, whereas all three components remain non-vanishing for ferromagnetic interactions. Specially, when the system is in the Tonks-Girardeau (TG) regime, obvious Fermi-like distribution emerges for each component. We also discuss the possible deviation of the spatial distribution from the Fermi-like distribution when the spin-spin interaction is strong enough.