Variation of the spin textures of 2-species spin-1 condensates studied beyond the single spatial mode approximation and the experimental identification of these textures

TL;DR

This paper investigates the complex spin textures in two-species spin-1 Bose-Einstein condensates using numerical solutions, classifies four distinct textures, and proposes experimental methods to identify and analyze these textures through probability densities.

Contribution

It introduces a simplified classification of spin textures beyond the single spatial mode approximation and links density measurements to texture transitions.

Findings

Identified four types of spin textures in two-species spin-1 condensates.

Demonstrated that density variations reflect spin-texture transitions.

Proposed experimental approaches to distinguish textures via probability densities.

Abstract

Based on the numerical solutions of the coupled Gross-Pitaevskii equations, the spin-textures of a Bose-Einstein condensate with two kinds of spin-1 atoms have been studied. Besides, the probability densities of an atom in spin component $\mu$ and of two correlated atoms one in $\mu$ and one in $\nu$ have been calculated. By an analysis of the densities, four types of texture have been found. (i) Both species are in polar phase. (ii) Both species are in ferromagnetic (f) phase with all the spins lying along a direction. (iii) Both species are in f phase but the spins of different species are lying along opposite directions. (iv) One species in f phase, one species in quasi-f phase (where the spins are divided into two groups lying along opposite directions). This finding simplifies the previous classification. Moreover, we found that the variation and transition of the spin-textures can be sensitively reflected by these probability densities. Therefore, the theoretical and experimental studies on these densities provide a way to discriminate the spin-textures and/or to determine the parameters (say, the strengths of interaction) involved.