Stable giant vortex annuli in microwave-coupled atomic condensates

Abstract

Stable self-trapped vortex annuli (VA) with large values of topological charge $S$ (giant VA) not only are a subject of fundamental interest, but are also sought for various applications, such as quantum information processing and storage. However, in conventional atomic Bose-Einstein condensates (BECs) VA with $S>1$ are unstable. Here we demonstrate that robust self-trapped fundamental solitons (with $S=0$) and bright VA (with the stability checked up to $S=5$) can be created in the free space by means of the local-field effect (the feedback of the BEC on the propagation of electromagnetic waves) in a condensate of two-level atoms coupled by a microwave (MW) field, as well as in a gas of MW-coupled fermions with spin $1/2$. The fundamental solitons and VA remain stable in the presence of an arbitrarily strong repulsive contact interaction (in that case, the solitons are constructed analytically by means of the Thomas-Fermi approximation). Under the action of the attractive contact interaction with strength $\ensuremath{\beta}$, which, by itself, would lead to collapse, the fundamental solitons and VA exist and are stable, respectively, at $\ensuremath{\beta}<{\ensuremath{\beta}}_{max}(S)$ and $\ensuremath{\beta}<{\ensuremath{\beta}}_{\mathrm{st}}(S)$, with ${\ensuremath{\beta}}_{\mathrm{st}}(S=0)={\ensuremath{\beta}}_{max}(S=0)$ and ${\ensuremath{\beta}}_{\mathrm{st}}(S\ensuremath{\ge}1)<{\ensuremath{\beta}}_{max}(S\ensuremath{\ge}1)$. Accurate analytical approximations are found for both ${\ensuremath{\beta}}_{\mathrm{st}}$ and ${\ensuremath{\beta}}_{max}$, with ${\ensuremath{\beta}}_{\mathrm{st}}(S)$ growing linearly with $S$. Thus, higher-order VA are more robust than their lower-order counterparts, in contrast to what is known in other systems that may support stable self-trapped vortices. Conditions for the experimental realizations of the VA are discussed.