Bogoliubov Theory and Lee-Huang-Yang Corrections in Spin-1 and Spin-2 Bose-Einstein Condensates in the Presence of the Quadratic Zeeman Effect

TL;DR

This paper develops Bogoliubov theory and calculates Lee-Huang-Yang corrections for spin-1 and spin-2 Bose-Einstein condensates under quadratic Zeeman effects, analyzing phase stability and symmetry-breaking phenomena.

Contribution

It introduces a comprehensive Bogoliubov framework for spinor BECs with quadratic Zeeman effects and explores the relationship between symmetry breaking and Nambu-Goldstone modes.

Findings

Derived LHY corrections for ground-state energy, sound velocity, and depletion.

Identified special Bogoliubov modes in the spin-2 nematic phase.

Analyzed phase stability against quantum fluctuations and Zeeman effects.

Abstract

We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.