Collective excitations in cigar-shaped spin-orbit coupled spin-1 Bose-Einstein condensates

TL;DR

This paper investigates the collective excitations in a spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a cigar-shaped trap, revealing how spin-orbit coupling and temperature influence density and spin modes.

Contribution

It provides a theoretical analysis of collective modes in spin-orbit-coupled spin-1 BECs, including analytical and numerical results at zero and finite temperatures.

Findings

Degeneracy of spin modes is broken by spin-orbit coupling.

Density and spin excitations behave differently with temperature.

Analytical results agree well with numerical simulations.

Abstract

We theoretically study the collective excitations of a spin-orbit-coupled spin-1 Bose-Einstein condensate with antiferromagnetic spin-exchange interactions in a cigar-shaped trapping potential at zero and finite temperatures using the Hartree-Fock-Bogoliubov theory with Popov approximation. The collective modes at zero temperature are corroborated by the real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We have also calculated a few low-lying modes analytically and found a very good agreement with the numerical results. We confirm the presence of excitations belonging to two broad categories, namely density, and spin excitations, based on the calculation of dispersion. The degeneracy between a pair of spin modes is broken by the spin-orbit coupling. At finite temperature, spin and density excitations show qualitatively different behavior as a function of temperature.