Thermal effects on the spin domain phases of high spin-f Bose-Einstein condensates with rotational symmetries

TL;DR

This paper investigates how thermal effects influence the spin phase domains of high-spin Bose-Einstein condensates, providing analytical tools to understand phase stability and magnetic properties at finite temperatures.

Contribution

It introduces a novel analytical framework combining Hartree-Fock and Majorana stellar representation to analyze thermal effects on spinor BECs with various symmetries.

Findings

Derived analytical expressions for the eigenspectrum of the thermal cloud.

Mapped the temperature-dependent regions of different spin phases.

Analyzed the behavior of multipolar magnetic moments with temperature.

Abstract

Spinor Bose Einstein condensates (BEC) can be realized nowadays using different atomic species of several spin values, offering unprecedented opportunities to scrutinize the underlying physics of its spin phase domains and of its quantum phase transitions. At sufficient low temperatures, lower than the critical temperature, a fraction of thermally excited atoms of the condensate can still interact with the whole system leading to spin-dependent interactions that can modify the nature of its phase domains. In this work, we characterize the thermal fraction of atoms of a spinorial BEC of general spin-$f$ value, provided that its ground state lies in a given spin phase with rotational symmetry. To that end, we use the Hartree-Fock approximation and a method based on the Majorana stellar representation for mixed quantum states and symmetry arguments. We consider the spin phases with usual point group symmetries, including those with some exotic phases associated to the platonic solids. The method leads to useful analytical expressions of the eigenspectrum of the thermal cloud allowing us to study the admissible regions and multipolar magnetic moments of the spin phases as a function of the temperature for general spin values.