Abstract
We demonstrate a possibility to generate localized states ineffectively one-dimensional Bose-Einstein condensates with anegative scattering length in the form of a dark soliton in thepresence of an optical lattice (OL) and/or a parabolic magnetictrap. We connect such structures with twisted localized modes(TLMs) that were previously found in the discrete nonlinearSchrödinger equation. Families of these structures are foundas functions of the OL strength, tightness of the magnetic trapand chemical potential, and their stability regions areidentified. Stable bound states of two TLMs are also found. Inthe case when the TLMs are unstable, their evolution isinvestigated by means of direct simulations, demonstrating thatthey transform into large-amplitude fundamental solitons. Ananalytical approach is also developed, showing that two orseveral fundamental solitons, with the phase shift π betweenadjacent ones, may form stable bound states, with parametersquite close to those of the TLMs revealed by simulations. TLMstructures are also found numerically and explained analytically in the case when the OL is absent, the condensate being confinedonly by the magnetic trap.
Highlights
The current experimental and theoretical studies of Bose-Einstein condensates (BECs) [1] have attracted a great deal of interest to nonlinear patterns which can exist in them, including dark [2] and bright [3] solitons
In this work we demonstrate that another type of localized nonlinear excitations, which may be regarded as dark solitons embedded in bright ones, can be created in attractive BECs
In this work we have demonstrated that counterparts of twisted localized modes (TLMs), which were earlier found in the discrete one-dimensional NLS equation, can exist as robust objects in attractive, effectively one-dimensional BoseEinstein condensates (BECs), provided that the condensate is confined by the optical lattice (OL) and/or parabolic magnetic trap
Summary
The current experimental and theoretical studies of Bose-Einstein condensates (BECs) [1] have attracted a great deal of interest to nonlinear patterns which can exist in them, including dark [2] and bright [3] solitons. Two-dimensional (2D) excitations in the form of vortices were realized experimentally [4] Other nonlinear excitations, such as Faraday waves [5], ring dark solitons and vortex necklaces [6] were predicted to occur in BECs. The behavior of the condensate crucially depends on the sign of the atomic interactions: dark (bright) solitons can be created in BECs with repulsive (attractive) interactions, resulting from the positive (negative) scattering length. [8], since we focus on the case of BECs with negative scattering length (such as 7Li [10] and 85Rb [11]), and demonstrate robustness and stability of TLMs in the latter context These structures, if regarded as effectively dark solitons in the attractive BEC, are the inverse of recently predicted [12] bright solitons in repulsive BECs with an optical lattice.
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