Phase transition between two-component and three-component ground states of spin-1 Bose-Einstein condensates

TL;DR

This paper mathematically proves the phase transition in spin-1 Bose-Einstein condensates from two-component to three-component ground states under a magnetic field, confirming previous numerical and experimental observations.

Contribution

It provides a rigorous mathematical proof of the phase transition phenomenon in spin-1 BECs, based on a principle related to mass density redistribution and kinetic energy reduction.

Findings

Confirmed the phase transition from two- to three-component states at a critical magnetic field.

Provided a mathematical proof supporting numerical and experimental results.

Demonstrated the role of mass density redistribution in energy minimization.

Abstract

For an antiferromagnetic spin-1 Bose-Einstein condensate under an applied uniform magnetic field, its ground state $(\psi_1,\psi_0,\psi_{-1})$ undergoes a phase transition from a two-component state ($\psi_0 \equiv 0$) to a three-component state ($\psi_j\ne 0$ for all $j$) at a critical value of the magnetic field. This phenomenon has been observed in numerical simulations as well as in experiments. In this paper, we provide a mathematical proof based on a simple principle found by the authors: a redistribution of the mass densities between different components will decrease the kinetic energy.