Self-consistent spin waves in magnetized BEC

TL;DR

This paper develops quantum hydrodynamic equations for magnetized spin-1 Bose-Einstein condensates, deriving a Gross-Pitaevskii equation and analyzing collective excitations, revealing a second spin wave mode and differences from electrically polarized BEC.

Contribution

It introduces a self-consistent quantum hydrodynamic framework for magnetized BEC, including spin-spin interactions, and derives a new Gross-Pitaevskii equation under specific conditions.

Findings

Existence of a second spin wave mode in magnetized BEC

Magnetization significantly alters wave dispersion properties

Derived equations unify magnetic and quantum effects in BEC

Abstract

We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account spin-spin interaction along with the short range interaction. We consider self-consistent field approximation of QHD equations. Starting from QHD equation we derive the Gross-Pitaevskii equation for magnetized BEC. We show that Gross-Pitaevskii equation exists under condition that the magnetic moment direction is not change. Using obtained QHD equations we study the dispersion of collective excitation. As in electrically polarized BEC [P. A. Andreev, L. S. Kuz'menkov, arXiv: 1201.2440], in the magnetically polarized BEC there is second wave mode (polarization mode or spin wave), in addition to the Bogoliubov's mode. Second wave solution appears due to the magnetic moment evolution. The influence of magnetization on dispersion of Bogoliubov's mode is found. We found strong difference of dispersion properties of waves in magnetized BEC from electrically polarized BEC.