Investigation of modulational instability and solitons in Bose Einstein condensates

Abstract

In 1924 the Indian physicist S.N. Bose sent a paper to Einstein in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose?s theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved. In the same year, Einstein predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this novel phenomenon, called Bose-Einstein condensation, will occur only for ?bosons?. Even though a lot of theoretical work has been done for many years on Bose Einstein condensates (BEC), only in 1995, this idea has been demonstrated in a series of experiments on vapors of alkali gas like 3Li, 23Na, and 85Rb in which the atoms confined in magnetic traps were cooled down to extremely low temperature of the order of micro Kelvin. Theoretical studies of trapped weakly interacting Bose gas have a long history. In this direction, in 1950, Gross and Pitaevskii carried out a pioneering work on the macroscopic wave function for BEC. This thesis deals with the modulational instability (MI) and theoretical study of soliton dynamics in a system of BEC under the appropriate physical conditions. The first chapter begins with the general introduction of Bose-Einstein condensation. Next, we discuss briefly for the fundamental particles like fermions and bosons. Next, we present and discuss several crucial concepts for understanding the phenomenon of non-interaction Bose gas. Further, we briefly discuss the experimental overview of BEC. Next, we discuss the theoretical background of weakly interacting dilute BEC and derive the Gross-Pitaevskii (GP) equation for the dynamics of the condensate. In the following discussion, we present collisional properties between the two atoms in the ultracold regime of atomic gases. Further, we discuss the physical properties of the condensates such as density, velocity of the condensate and approximate solution