Dinâmica de sólitons vetoriais em condensados de Bose-Einstein com interação spin-órbita

Abstract

Nowadays, the experimental realization of a Bose-Einstein condensate (BEC) of atoms with spin-orbit interaction (SOC) has aroused a new interest in studying the intriguing and interesting properties of the system. For example, a BEC of 87Rb atoms (with atomic hyper ne state f = 1) trapped in cigar form (quasi-one-dimensional) can be subjected to an external magnetic eld, which causes the Zeeman e ect on the states of its constituent atoms. Then, through of an arrangement of Raman-type laser and a certain frequency of the lasers, it is possible to induce a transition between the sub-levels mf = 􀀀1 and mf = 0, thus leading to spin-orbita coupling, between the hyper ne sub-levels, and a mixture of states for each sub-level. In this dissertation, we study several dynamics of the bright-bright vector soliton, in (1 + 1) space-time dimensions, which are created in a BEC of two internal state atoms, with and without spin-orbit coupling, governed by two equations of Gross-Pitaevskii coupled. To solve the coupled equations, we employed the variational approximation, being used recently for this type of system. In both cases, with and without spin-orbit coupling, we present exact analytical solutions, which solve the equations of motion with di erent polynomial potentials. From the analytical solutions, we study the precession of the system pseudo-spin vector S = 1=2, the unbalance of the pseudo-spin Sz of the soliton, the phase di erence between the soliton components (internal dynamics of soliton), in addition, we also study the movement of the center of mass of the system, and the evolution of the linear momentum of the system (external dynamics of the soliton). We explicitly show the in uence of external potential on the pseudo-spin precission of the system. Finally, we study numerically the stability conditions of the bright-bright soliton solutions, obtained in this work, under small disturbances in their initial condition.