Interaction of solitons with localized potential wells in nonlinear optics and Bose-Einstein condensates

Abstract

The interplay of particle and wave properties of soliton has triggered great interest in a fundamental understanding of the implication of quantum mechanics. A better understanding of wave-particle duality in physics could lead to a new and exciting theoretical research and encouraging experimentalists that exploit their quantum nature. As an example of such a system, in this thesis, we investigate the interaction of solitons in Bose-Einstein condensate and nonlinear optic with localized potential well in the different physical setting. The phenomena of reflection, trapping and transmission of an incident soliton are predicted to occur by varying the initial velocity (kinetic energy). To achieve the objective, we construct analytical and numerical studies of the interaction of a spatial soliton on an interface between two nonlinear media, when both cubic and quintic nonlinearity will be considered. Then, we analyse the effect of Gaussian potential on the scattering of the vector soliton in a Coupled Nonlinear Schrodinger Equation. Lastly, we investigate numerically the role of bound states in the potential well on the result of scattering of NLSE soliton with Gaussian potential well. The main analytical tool will be the variational approximation method. It was used to analyse the dynamics of the width and centre of mass position of soliton during the scattering process. The accuracy of approximations is verified by direct numerical simulations of the governing equation. We find a good agreement between the numerical results and the analytical results. The result has shown that the soliton can be fully trapped by the potential well due to resonances with the bound states. Plus, the quantum reflection occurs where the soliton is sufficiently slow such that the nonlinear energy dominates over the kinetic energy and a sharp transition to transmission above the critical value of the velocity is identified.