Stable giant vortex annuli in microwave-coupled atomic condensates

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 β, which, by itself, would lead to collapse, the fundamental solitons and VA exist and are stable, respectively, at β<βₘₐₓ(S) and β<βₛₜ(S), with βₛₜ(S=0)=βₘₐₓ(S=0) and βₛₜ(S≥1)<βₘₐₓ(S≥1). Accurate analytical approximations are found for both βₛₜ and βₘₐₓ, with βₛₜ(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.