Berezinskii-Kosterlitz-Thouless transition of spin-1 spinor Bose gases in the presence of the quadratic Zeeman effect

Abstract

We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and ${\mathbb{Z}}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.

15 pages, 19 figures

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• Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions
• Dipolar and spinor bosonic systems
• Cluster representations and the Wolff algorithm in arbitrary external fields
• Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties
• Fractional-flux vortices and spin superfluidity in triplet superconductors
• Quantum field theory of nematic transitions in spin orbit coupled spin-1 polar bosons

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• Anomalous phase ordering of a quenched ferromagnetic superfluid
• Vortex confinement transitions in the modified Goldstone model
• Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid
• Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate
• ${\mathbb{Z}}_n$ modified XY and Goldstone models and vortex confinement transition
• Berezinskii-Kosterlitz-Thouless transitions in a ferromagnetic superfluid: effects of axial magnetization
• Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin
• Dynamics of Polar-Core Spin Vortices in Inhomogeneous Spin-1 Bose-Einstein Condensates