Magnetic phases and phase diagram of spin-1 condensate with quadrupole degrees of freedom

TL;DR

This paper develops a comprehensive Hamiltonian for spin-1 Bose-Einstein condensates incorporating quadrupole degrees of freedom, analyzes their phase diagram, and explores how these degrees influence physical properties and excitations.

Contribution

It introduces a Hamiltonian including quadrupole degrees of freedom for spin-1 atoms and applies it to study phase behavior and excitations in condensates, extending previous models.

Findings

Identification of ferromagnetic, quadrupolar, and paramagnetic phases.

Construction of the phase diagram including quadrupole effects.

Analysis of how quadrupole degrees modify excitation spectra.

Abstract

We obtain and justify a many-body Hamiltonian of pairwise interacting spin-1 atoms, which includes eight generators of the SU(3) group associated with spin and quadrupole degrees of freedom. It is shown that this Hamiltonian is valid for non-local interaction potential, whereas for local interaction specified by $s$-wave scattering length, the Hamiltonian should be bilinear in spin operators only (of the Heisenberg type). We apply the obtained Hamiltonian to study the ground-state properties and single-particle excitations of a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate taking into account the quadrupole degrees of freedom. It is shown that the system under consideration can be in ferromagnetic, quadrupolar, and paramagnetic phases. The corresponding phase diagram is constructed and discussed. The main characteristics such as the density of the grand thermodynamic potential, condensate density, and single-particle excitation spectra modified by quadrupole degrees of freedom are determined in different phases.