Ground state patterns and phase transition of spin-1 Bose-Einstein condensates via \Gamma-convergence theory

TL;DR

This paper analytically characterizes the ground state patterns and phase transitions of spin-1 Bose-Einstein condensates under magnetic fields, revealing interface properties and phase diagrams using b3-convergence theory.

Contribution

It develops a comprehensive analytical framework for understanding ground state configurations and phase transitions in spin-1 BECs, including interface behavior and phase diagrams.

Findings

Identifies four basic ground states: magnetic, nematic, two-component, three-component.

Derives a complete phase diagram for different magnetic field strengths and magnetizations.

Shows interfaces have constant mean curvature and contact angles follow Young's relation.

Abstract

We develop an analytic theory for the ground state patterns and their phase transitions for spin-1 Bose-Einstein condensates on a bounded domain in the presence of a uniform magnetic field. Within the Thomas-Fermi approximation, these ground state patterns are composed of four basic states: magnetic state, nematic state, two-component state and three-component state, separated by interfaces. A complete phase diagram of the ground state patterns are found analytically with different quadratic Zeeman energy q and total magnetization M for both ferromagnetic and antiferromagnetic systems. Using the \Gamma-convergence technique, it is found that the semi-classical limits of these ground states minimize an energy functional which consists of interior interface energy plus a boundary contact energy. As a consequence, the interface between two different basic states has constant mean curvature, and the contact angle between the interface and the boundary obeys Young's relation.