Analytical Study Of Soliton Dynamics In Bose Einstein Condensates

Bose-Einstein condensation（BEC）is widely used in condensed matter physics,quantum information and quantum computing.And the soliton plays an important role in the nonlinear science because solitons could maintain their original shape to transmit stably in the transmission process.The discovery of the BEC provides a good platform for the study of solitons.However,the study of solitons in the BEC mainly depends on the numerical calculation at present,it lacks the corresponding analytical research and experimental analysis,and there is still a lack of comprehensive analysis.In this paper,with the help of quantum statistical mechanics analysis of the BEC,based on three kinds of nonlinear Schr?dinger（NLS）equations,the soliton solutions of those equations are obtained by the bilinear method and auxiliary function method,and the nonlinear dynamical behavior of solitons under different conditions is analyzed.Moreover the soliton interaction in the BEC and the conditions for the stable existence of solitons in the BEC system are studied,and the stability of the soliton coherence evolution in the BEC is ensured.Finally,according to the theoretical results obtained in this paper,the corresponding fiber laser experimental scheme is formulated,and the Qswitched laser output is realized,which provides experimental support for analyzing the nonlinear mechanism of solitons in the BEC system.The details are as follows:（1）Based on the second-order NLS equation with variable coefficients,the stable transmission of dark solitons and single solitons with double peaks in the BEC system is realized,the anti-dark soliton is obtained,and the anti-dark soliton interactions under four different group velocity dispersion（GVD）parameters are systematically analyzed.The dark soliton transmission in the inhomogeneous optical fibers is studied.When the GVD coefficient is the hyperbolic tangent function,the V-type solitons are obtained,and the corresponding influence of various effects on the V-type soliton transmission is analyzed.The production and transmission of stable single solitons with double peaks are studied.When the GVD coefficient is sinusoidal function,the behavior of single solitons with double peaks is periodic transmission.The method of weakening the optical soliton interaction is studied,and the effective control of the optical soliton interaction is realized.（2）Based on the third-order NLS equation with variable coefficients,the dynamic characteristics of the generation and interaction of M-type dark solitons are studied.The influence of the group velocity dispersion and nonlinearity effects on the M-type dark soliton transmission in the optical fiber is analyzed.The interaction time and strength of solitons are controlled by adjusting the corresponding parameters.Effects of the GVD and third-order dispersion on the soliton interaction are discussed.Finally,The function of the all-optical switching is realized by the interaction analysis,the strength and switch logic of the all-optical switching are effectively controlled.（3）Based on the fifth-order variable coefficients NLS equation,the influence of higher-order effects on the generation of solitons and soliton interaction is analyzed.Influences of relevant parameters on the single soliton generation is analyzed,and the effective control of the soliton phase,amplitude,transmission speed and transmission path is realized.The transmission of solitons along the M-type curve and the functions ofsoliton compression and soliton amplification are realized.By controlling the spacing of solitons,the regulation of the soliton interaction is realized.（4）The effects of the tungsten disulfide film and molybdenum selenide film on the generation and transmission characteristics of solitons in fiber lasers are analyzed.The tungsten disulfide（WS2）SA is prepared by the microstructure fiber,and the corresponding nonlinear optical properties of WS2 are verified.Based on the those properties of the WS2 SA,transmission characteristics of solitons in the fiber laser are analyzed.The SA based on the molybdenum diselenide（MoSe₂）with the high quality and high optical property is prepared,and the stable Q-switched fiber laser output is realized.This paper is devoted to the analysis and experimental research of various NLS equations in the BEC system.The conclusions obtained have the high value of research.The research of this subject has guiding significance in the study of solitons in the BEC,and is good for thefurther development of low temperature physics,nonlinear science and other related fields.