Abstract
Modulational instability conditions for the generation of localized structures in the context of matter waves in Bose-Einstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.
Highlights
Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations
Bose-Einstein condensates (BEC) made of ultracold atomic alkali gases have proven to be a fertile field in the last years for the study of nonlinear matter waves in recent reviews and monographs [1,2]
A generic theoretical model widely employed involves the Gross-Pitaevskii (GP) equation, which bears the form of a nonlinear Schrödinger-type equation with a cubic nonlinearity, taking into account boson interactions, in addition to the confinement potential imposed on the BEC in a potential trap
Summary
Bose-Einstein condensates (BEC) made of ultracold atomic alkali gases have proven to be a fertile field in the last years for the study of nonlinear matter waves in recent reviews and monographs [1,2]. The scattering length as, initially taken to be positive (accounting for repulsive interactions and prescribing condensate stability), has later been sign-inverted to negative (attractive interaction) via Feshbach resonance, in appropriately designed experiments This allowed for the prediction of BEC state instability, eventually leading to wave collapse, which is only possible in the attractive case as 0 [3]. For higher densities or stronger confinement, it has become clear that a better description of atom-atom interaction will be required For homogeneous systems, it has been demonstrated in a recent work by Cowell et al [7] that different potentials having the same scattering length can lead to a vastly different ground-state energy. The principal objet of this paper is to show analytically conditions stability for the generation of localized structures in BEC via MI and to discuss the comparison between the linear analysis of plane wave solutions and the direct numerical simulations of the full modified GP equation
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