An inequality for spinor Bose-Einstein condensates

TL;DR

This paper derives a new inequality relating density, singlet pair amplitude, and magnetization in spin-F Bose-Einstein condensates, providing insights into high-symmetry spinor distributions using Majorana representation.

Contribution

It introduces a novel inequality for spinor BECs that constrains their physical parameters and explores the distribution of high-symmetry states with a geometric representation.

Findings

The inequality constrains the parameters of spin-F BECs.

Majorana representation elucidates high-symmetry spinor distributions.

Illustration with spin-2 BECs demonstrates the inequality's application.

Abstract

An inequality for spin-$F$ Bose-Einstein condensates (BECs) $ F^2(\rho^2-|\Theta|^2)-\boldsymbol{M}^2\ge0 $ is reported, where $\rho$, $\Theta$, and $\boldsymbol{M}$ represent the density, singlet pair amplitude, and magnetization vector, respectively. The distribution of high-symmetry spinors in the allowed region by the inequality is elucidated with using the Majorana representation. The result is illustrated by the example of spin-2 BECs.