Mesoscopics of half-quantum vortex pair deconfinement in a trapped spin-one condensate

TL;DR

This paper investigates the stability and deconfinement of half-quantum vortices in a spin-1 Bose-Einstein condensate, revealing how system parameters influence vortex dissociation and phase transitions.

Contribution

It introduces a critical ratio of coupling constants determining vortex deconfinement, dependent on system size, trap potential, and interaction parameters, with implications for experimental control.

Findings

Critical coupling ratio for vortex dissociation derived.

Vortex dissociation favored for negative c2, blocked for positive c2.

Deconfinement transition depends on system size and trap type.

Abstract

Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein condensate of ${}^{23} \textrm{Na}$ atoms, we study the energetical stability of a singly quantum vortex injected into the center of a quasi-two-dimensional gas with zero total spin against dissocation into a pair of half-quantum vortices. We find that the critical dissociation point of this confinement-deconfinement type phase transition can be expressed in terms of the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants. The transition of bound to unbound vortices, in particular, sensitively depends on (1) the ratio of system size ($R$) to density healing length ($\xi_d$), and (2) the trap potential. Specifically, the critical ratio $(c_2 / c_0)_{\textrm{cr}}$ increases when $R / \xi_d$ decreases, and is relatively larger in a harmonic trap than in a box trap. Dissociation is energetically generally favored for $c_2 / c_0 < (c_2 / c_0)_{\textrm{cr}}$, which as a corollary implies that vortex dissociation is observed as well for negative $c_2 < 0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC ($c_2>0$) it is energetically blocked above the critical ratio $(c_2 / c_0)_{\textrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave control techniques, the dependence of the deconfinement phase transition on coupling parameters, density, and system size we predict, can be verified in experiments with ultracold spinor gases.