Stable giant vortex annuli in microwave-coupled atomic condensates

Abstract

Stable self-trapped vortex annuli (VAs) with large values of topological charge S (giant VAs) are not only 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) VAs with S > 1 are unstable. Here, we demonstrate that robust self-trapped fundamental solitons (with S = 0) and bright VAs (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 VAs 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 VAs 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 VAs are more robust than their lower-order couterparts, on the contrary to what is known in other systems that may support stable self-trapped vortices. Conditions for the experimental realizations of the VAs are discussed.

(INVITED) Vortex solitons: Old results and new perspectives

“…22(a). It is worthy to note that prediction (86) does not depend on strength γ of the effective long-range interaction, because this coefficient appears only as an overall factor in expression (85), and it remains valid in the limit of γ → 0, i.e., for the usual two-dimensional NLSE with the local cubic self-attractive term,…”

“…The stability of the solitons was identified by real-time simulations of Eqs. (77) and (78) with random perturbations added to the initial conditions (independent perturbations were taken for φ ↑ and φ ↑ , to verify the stability against breaking the equality of the two components) [85]. The fundamental solitons (S = 0) are stable in their entire existence region, β < β collapse (S = 0) ≈ 11.8 (in the present notation, it is tantamount to the TS norm, see Eq.…”

“…For the vortex solitons with S ≥ 1, the numerical analysis reveals an internal stability boundary, β stability (S) < β collapse (S), the vortices being stable at β < β stability (S), see Table 1. In the interval of β stability (S) < β < β collapse (S), they are broken by azimuthal perturbations into rotating necklace-shaped clusters of fragments, which resembles the initial stage of the instability development of localized vortices in usual models; however, unlike those models [244][245][246] The stability boundary, β stability (S), can be found in an approximate analytical form too [85]. To this end, the wave function of an azimuthally perturbed vortex ring is approximated by…”

“…[35], soon after the concept of the TS was established; while such states are unstable, they can be stabilized by means of the "management" technique, which makes the coefficient of the cubic nonlinearity a periodically varying function of t [36]). Recently, an analytical approximation was developed, which produces values N (S) TS for S ≥ 1 with a good accuracy [85], see Eq. (86) and Table II below.…”

“…Two other topics in the review present entirely recent developments. These are schemes for the creation of stable 2D and 3D solitons in models of binary BEC, with its two components interacting by means of the spin-orbit coupling (SOC) [80][81][82], or through a resonant microwave field [85]. The latter section also briefly outlines results for vortex solitons obtained in other models with effectively nonlocal nonlinearities.…”