Dynamics of bose einstein condensate in linear and non linear regime

Abstract

The fascinating eld of exploring non linear systems exhibits rich dynamicsand these systems are found in almost every part of nature whether it isthe periodic beating of the heart the ripples of sand dunes complex shapesin snowakes or the existence of stripes on Jupiter and on animals Beyondrich spatial and temporal patterns nonlinearity present in any systemcan lead to the formation and evolution of localized structures which haveunusual features such as solitons and vortices Solitons are spatially localized structures or waves which arise due to thebalance of dispersion and nonlinearity in a system These structures maintaintheir shape during propagation are remarkably stable against any perturbationsor mutual collision and show particle like properties In general solitons underlie the understanding of tidal bores cyclones massive oceanwaves like tsunamis signal conduction in neurons and natural phenomenasuch as Morning Gloryquot hundreds of kilometers of cloud waves Solitonshave been actively studied in many di erent domains including in mathematicsand physics such as in the context of the solution of the Korteweg deVries equation in shallow water in magnetic thin lms and optical bers Solitons have given a massive impetus to today s telecommunications industrydue to the ability of optical pulses to propagate as solitons for vastdistances without signi cant loss or dispersion In this thesis we explored through experiments and numerical simulations the behaviour and dynamics of the Bose Einstein Condensate BEC in twodi erent regimes linear interactions in the system are negligible and nonlinearregime interactions in the system becomes dominant A BEC ofdilute atomic vapor not only provides a clean and well controlled environmentto study a variety of physics problems of superuid systems including solitons and vortices but also o newline newline