Field induced phase segregation and collective excitations of a trapped spinor Bose-Einstein condensate

TL;DR

This paper investigates the phase segregation and collective excitations in a trapped spinor Bose-Einstein condensate under a magnetic field, revealing coexistence of polar and ferromagnetic phases and analyzing their excitation spectra.

Contribution

It introduces a hydrodynamic model for spinor BECs under magnetic fields, showing phase segregation and deriving analytical solutions for excitation spectra.

Findings

Polar and ferromagnetic phases coexist and are spatially segregated.

Excitation spectra are unaffected by magnetic field within the Thomas-Fermi approximation.

Analytical solutions for excitation spectra in isotropic traps are obtained.

Abstract

A hydrodynamic description is used to study the zero-temperature properties of a trapped spinor Bose-Einstein condensate in the presence of a uniform magnetic field. We show that, in the case of antiferromagnetic spin-spin interaction, the polar and ferromagnetic configurations of the ground state can coexist in the trap. These two phases are spatially segregated in such a way that the polar state occupies the inner part while the ferromagnetic state occupies the outer part of the atomic cloud. We also derive a set of coupled hydrodynamic equations for the number density and spin density excitations of the system. It is shown that these equations can be analytically solved for the system in an isotropic harmonic trap and a constant magnetic field. Remarkably, the related low lying excitation spectra are completely determined by the solutions in the region occupied by the polar state. We find that, within the Thomas-Fermi approximation, the presence of a constant magnetic field does not change the excitation spectra which still possess the similar form of that obtained by Stringari.