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 <β_max(S ) and β <β_st(S ) , with β_st(S =0 ) =β_max(S =0 ) and β_st(S ≥1 ) <β_max(S ≥1 ) . Accurate analytical approximations are found for both β_st and β_max, with β_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.