Vortex Excitations of Dirac Bose-Einstein Condensates

TL;DR

This paper investigates vortex states in non-equilibrium Dirac Bose-Einstein condensates, revealing unique multi-component vortex structures, the influence of a Haldane gap, and mapping their phase diagram through numerical methods.

Contribution

It introduces a detailed analysis of vortex configurations in Dirac BECs, highlighting the effects of phase winding differences and the Haldane gap, and provides a comprehensive phase diagram.

Findings

Identified three classes of vortex states with distinct far-field behaviors.

Discovered multiple core vortices due to phase winding differences.

Mapped the phase diagram of topological sectors in Dirac BECs.

Abstract

We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find that the multi-component structure of Dirac equation enables the difference in phase winding of two condensates with respective phase winding number differing by one, $\ell_a - \ell_b = \pm 1$. We observe three classes of vortex states distinguished by their far-field behavior: A ring soliton on either of the two components in combination with a vortex on the other component, and, in the case of strong inter-component interactions, a vortex profile on both components. The latter are multiple core vortices due to the phase winding difference between the components. We also address the role of a Haldane gap on these vortices, which has a similar effect than inter-component by making the occupation on either sublattice more costly. We employ a numerical shooting method to reliably identify vortex solutions and use it to scan large parts of the phase space. We then use a classification algorithm on the integrated wavefunctions to establish a phase diagram of the different topological sectors.