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Communications in Theoretical Physics

Effects of Quantum Fluctuations on P T -Symmetric Solitons of a Trapped Bose Gas*

Wei 伟 Qi 漆, Liangwei Dong, Hai-Feng 海凤 Li 李

Published Jul 1, 2019• 1 citation
Publisher

Abstract

Abstract Considering the quantum fluctuation effects, the existence and stability of solitons in a Bose-Einstein condensate subjected in a P T -symmetric potential are discussed. Using the variational approach, we investigate how the quantum fluctuation affects the self-localization and stability of the condensate with attractive two-body interactions. The results show that the quantum fluctuation dramatically influences the shape, width, and chemical potential of the condensate. Analytical variational computation also predicts there exists a positive critical quantum fluctuation strength q c with each fixed attractive two-body interaction g 0 , if the quantum fluctuation strength q 0 is bigger than q c , there is no bright soliton solution existence. We also study the effects of the quantum fluctuations on the stability of solitons using the Vakhitov-Kolokolov (VK) stability criterion. A robust stable bright soliton will always exist when the quantum fluctuation strength q 0 belongs to the parameter regimes q c ≥ q 0 > 0.

DOI
10.1088/0253-6102/71/7/773

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Abstract Considering the quantum fluctuation effects, the existence and stability of solitons in a Bose-Einstein condensate subjected in a P T -symmetric potential are discussed. Using the variational approach, we investigate how the quantum fluctuation affects the self-localization and stability of the condensate with attractive two-body interactions. The results show that the quantum fluctuation dramatically influences the shape, width, and chemical potential of the condensate. Analytical variational computation also predicts there exists a positive critical quantum fluctuation strength q c with each fixed attractive two-body interaction g 0 , if the quantum fluctuation strength q 0 is bigger than q c , there is no bright soliton solution existence. We also study the effects of the quantum fluctuations on the stability of solitons using the Vakhitov-Kolokolov (VK) stability criterion. A robust stable bright soliton will always exist when the quantum fluctuation strength q 0 belongs to the parameter regimes q c ≥ q 0 > 0.
Variational Approach to Study PT{\mathscr{P}}{\mathscr{T}}PT-Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions
Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a - symmetric potential are discussed. In the framework of the variational approach, we investigate how the non-locality of interactions affects the self-localization and stability of a condensate with attractive two-body interactions. The results reveal that the non-locality of interactions dramatically influences the shape, width, and chemical potential of the condensate. Analytically variational computation also predicts that there exists a critical negative non-local interaction strength ( p c < 0) with each fixed two-body interaction ( g 0 < 0), and there exists no bright soliton solution for p 0 < p c . Furthermore, we study the effect of the non-locality interactions on the stability of the solitons using the Vakhitov–Kolokolov stability criterion. It is shown that for a positive non-local interaction ( p 0 > 0), there always exist stable bright solitons in some appropriate parameter regimes .
Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.
We employ mean-field, Bogoliubov and many-body theories to study critical fluctuations in the position and momentum of a Bose-Einstein condensate whose translation symmetry is spontaneously broken due to attractive interactions. In a homogeneous system, the many-body ground state of the symmetry-preserving Hamiltonian is very fragile against superposition of low-lying states, while the mean-field theory predicts a stable bright soliton which spontaneously breaks translation symmetry. We show that weak symmetry-breaking perturbations cause the translation-symmetric many-body ground state to cross over to a many-body bright soliton. We argue that the center-of-mass fluctuations in the soliton state arise primarily from the depletion of the condensate to translation modes. We develop an extended mean-field theory to analytically reproduce these results obtained by the exact diagonalization method.
We study the ground-state properties of a one-dimensional Bose gas with NNN-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schr\"odinger equation, we compute the chemical potential and the ground-state energy. For N=3N=3N=3, a localized soliton wave function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parametrized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of NNN-body attractive contact interactions in higher dimensions is presented.
We consider a Bose-Einstein condensate (BEC) with non-local inter-particle interactions. The local Gross-Pitaevskii (GP) equation is valid for the gas parameter [Formula: see text], but for [Formula: see text], the BEC is described by a modified GP equation (MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter (ν) on the stability of the solitons using the Vakhitov-Kolokolov (VK) stability criterion. We show that these soliton solutions are stable according to the VK criterion. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.