Excited spin states and phase separation in spinor Bose-Einstein condensates

TL;DR

This paper investigates the structure and phase behavior of spin-1 Bose-Einstein condensates under magnetic fields, revealing conditions for phase separation in polar condensates and stability in ferromagnetic ones, supported by theoretical and numerical analysis.

Contribution

It introduces a classification of stationary states, analyzes their bifurcations, and predicts phase separation in polar condensates based on energy concavity, supported by simulations.

Findings

Phase separation occurs in polar condensates' ground states.

Ferromagnetic condensates exhibit always miscible spin components.

Phase separation predicted in $^{23}$Na condensates in elongated traps.

Abstract

We analyze the structure of spin-1 Bose-Einstein condensates in the presence of a homogenous magnetic field. We classify the homogenous stationary states and study their existence, bifurcations, and energy spectra. We reveal that the phase separation can occur in the ground state of polar condensates, while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogenous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a $^{23}$Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.