Effects of Quantum Fluctuations on -Symmetric Solitons of a Trapped Bose Gas**Supported by the National Natural Science Foundation of China under Grant Nos. 11647017, 11805116, 21703166, and supported by Science Research Fund of Shaanxi University of Science and Technology under Grant No. BJ16-03

Abstract

Considering the quantum fluctuation effects, the existence and stability of solitons in a Bose-Einstein condensate subjected in a -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 qc with each fixed attractive two-body interaction g0, if the quantum fluctuation strength q0 is bigger than qc, 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 q0 belongs to the parameter regimes qc ≥ q0 > 0.