Simultaneous dipole and quadrupole moment contribution in the Bogoliubov spectrum: Application of the non-integral Gross-Pitaevskii equation

TL;DR

This paper develops a non-integral Gross-Pitaevskii equation for Bose-Einstein condensates with electric dipole and quadrupole moments, analyzing their combined effects on the Bogoliubov spectrum and stability.

Contribution

It introduces a coupled model for dipole and quadrupole interactions in BECs, extending the Bogoliubov spectrum analysis beyond dipolar systems.

Findings

Quadrupole-quadrupole interaction positively affects the spectrum.

The model predicts an additional term in the Bogoliubov spectrum.

The spectrum remains stable with combined dipole and quadrupole interactions.

Abstract

We present the Gross-Pitaevskii equation for Bose-Einstein condensates (BECs) possessing the electric dipole and the electric quadrupole moments in a non-integral form. These equations are coupled with the Maxwell equations. The model under consideration includes the dipole-dipole, the dipole-quadrupole, and the quadrupole-quadrupole interactions in terms of the electric field created by the dipoles and quadrupoles. We apply this model to obtain the Bogoliubov spectrum for three dimensional BECs with a repulsive short-range interaction. We obtain an extra term in the Bogoliubov spectrum in compare with the dipolar BECs. We show that the quadrupole-quadrupole interaction gives a positive contribution in the Bogoliubov spectrum. Hence this spectrum is stable.