Stochastic Gross-Pitaevskii theory for a spin-1 Bose gas: Application to superfluidity in two dimensions

TL;DR

This paper introduces a stochastic Gross-Pitaevskii framework for spin-1 Bose gases, analyzing equilibrium phases and superfluid behavior in two dimensions, including a novel phase with independent mass and spin superflows.

Contribution

It develops a stochastic projected Gross-Pitaevskii equation for spin-1 gases and identifies a new superfluid phase with independent mass and spin superflows.

Findings

Identification of three superfluid phases, including a novel phase with independent mass and spin superflows.

Finite-temperature phase diagram for ferromagnetic spin-1 Bose gas.

Characterization of phase transitions via vortex unbinding and spin-component densities.

Abstract

This paper develops and implements the stochastic projected Gross-Pitaevskii equation for spin-1 Bose gases, addressing key considerations for numerical simulations. As an application of the theory we explore equilibrium phases in a two-dimensional spin-1 gas, where quasi-long-range order emerges via a Berezinskii-Kosterlitz-Thouless transition. Our analysis includes definition of superfluid densities for both mass and spin degrees of freedom, in a manner suitable for implementation within a stochastic projected Gross-Pitaevskii equation simulation. We present a finite-temperature phase diagram for the ferromagnetic spin-1 Bose gas and identify three distinct superfluid phases: two exhibiting conventional Berezinskii-Kosterlitz-Thouless-like behavior and a novel phase that simultaneously supports independent mass and spin superflows. As temperature increases, the stability region of this novel phase shrinks. We provide characterization of the phase transitions through consideration of the spin-component densities and the unbinding of multiple types of vortices. This work provides a foundation for further studies of nonequilibrium and finite-temperature phenomena in spinor Bose gases.