Phases of a polar spin-1 Bose gas in a magnetic field

TL;DR

This paper investigates the phases of a polar spin-1 Bose gas under magnetic fields, exploring phase transitions and generalizing the Hugenholtz--Pines theorem within a mean field framework.

Contribution

It introduces a generalized Hugenholtz--Pines theorem for polar spin-1 gases and analyzes phase crossover and transitions at finite temperature and magnetization.

Findings

Identification of two Bose-Einstein condensed phases

Generalization of the Hugenholtz--Pines theorem

Analysis of quantum phase transition crossover

Abstract

The two Bose--Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz--Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation.