Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates

Abstract

We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with topological charge up to S = 6 (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with S). The largest nonlinearity-localization radius admitting the stabilization of the higher-order vortices is estimated analytically and accurately identified in a numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, S > 1, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.

Stable giant vortex annuli in microwave-coupled atomic condensates

“…The stability boundary, β st , is found in an approximate analytical form too. On the contrary to previously studied models [29,33,34], the (giant) VAs with higher vorticities, such as S = 5, are more robust than their counterparts with small S. In addition, a very accurate TFA (Thomas-Fermi approximation) was developed for the fundamental solitons, with S = 0. The results have been obtained for both symmetric and strongly asymmetric twocomponent systems.…”

“…On the other hand, under the action of an attractive contact interaction, with strength β, which drives the critical collapse in the 2D geometry [35], the VAs exist and are stable, respectively, for β < β max and β < β st ≤ β max . We demonstrate, by means of analytical and numerical considerations, that β st linearly grows with S, thus making higher-order vortices more robust than lower-order ones, opposite to what is known in few other models capable to support stable higherorder VAs [33,34]. It is relevant to mention that the concept of giant vortices is known in the usual BEC settings with the contact repulsion [36], where they are not self-trapped objects, i.e., they are not VAs.…”

“…The family of single-component modes with S = 1 may be partly stabilized by a trapping potential, but all the higher-order VAs with S ≥ 2 remain unstable in this case too [32]. Partly stable VAs with S ≥ 2 were predicted only in "exotic" settings, with the local strength of the repulsive nonlinearity in the space of dimension D growing with distance r from the center faster than r D [33], or making use of a combination of a trapping potential and a spatially localized attractive interaction [34].…”

Estabilidade de vórtices em condensados de Bose-Einstein

“…Como será discutido, com o tipo de interação em questão é possível estabilizar vórtices com valores de vorticidade de até S = 6, pelo menos. Tais resultados nunca foram observados experimentalmente ou previstos teoricamente, de modo que os mesmos foram recentemente publicados no periódico Physical Review A[64]. 4.2.1 Potencial químico e energia Do mesmo modo que na seção anterior, na presente seção é estudado um condensado sujeito a um connamento harmônico bidimensional.…”

“…64) conhecidas na literatura como Equações de Bogoliubov-de Gennes. Este sistema de equações é empregado neste trabalho para o estudo de estabilidade das soluções da equação de Gross-Pitaevskii, como será visto adiante.…”