Phase characterization of spinor Bose-Einstein condensates: a Majorana stellar representation approach

TL;DR

This paper introduces a novel Majorana stellar representation approach combined with group theory to analyze phase diagrams and perturbations in spinor Bose-Einstein condensates, simplifying the exploration of emergent phenomena.

Contribution

It presents a new method using Majorana stellar representation for mixed states to study phase characterization in spinor BECs, reducing complexity and enabling detailed phase analysis.

Findings

Characterized phases of spin-1 Bose-Einstein condensates.

Predicted non-linear temperature dependence of the cyclic-nematic phase boundary.

Applied the method to study entropy effects on phases.

Abstract

We study the variational perturbations for the mean-field solution of an interacting spinor system with underlying rotational symmetries. An approach based upon the Majorana stellar representation for mixed states and group theory is introduced to this end. The method reduces significantly the unknown degrees of freedom of the perturbation, allowing us a simplified and direct exploration on emergent physical phenomena. We apply it to characterize the phases of a spin-1 Bose-Einstein condensate and to study the behavior of these phases with entropy. The spin-2 phase diagram was also investigated within the Hartree-Fock approximation, where a non-linear deviation of the cyclic-nematic phase boundary with temperature is predicted.