Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

TL;DR

This paper theoretically investigates the magnetic phases of spin-1 Bose-Einstein condensates, emphasizing the role of quadrupole interactions and external magnetic fields in creating a broken-axisymmetry state and mapping the magnetic phase diagram.

Contribution

It introduces a comprehensive Hamiltonian including spin and quadrupole interactions, revealing new insights into the broken-axisymmetry state and magnetic phase diagrams of spin-1 condensates.

Findings

Identification of three regimes for preparing the broken-axisymmetry state.

Calculation of thermodynamic properties for various magnetic states.

Magnetic state diagrams illustrating phase transitions.

Abstract

We theoretically study a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also re-examine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential, as well as excitation energies for broken-axisymmetry state. We show that the broken-axisymmetry state can be prepared at three different regimes of applied magnetic field. We also present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.