Abstract
This thesis reports the theoretical progress of the properties and dynamics of electromagnetically induced transparency (EIT) and Bose-Einstein condensate. We develop a numerical scheme to include the atomic motions in the EIT medium and we apply the stochastic projected Gross-Pitaevskii equation to study the non-equilibrium dynamics in multi-component Bose condensates. In the part of EIT at non-zero temperature, by using the invariance of the Schr"{o}dinger equation under the Galilean transformation, we successively include the atomic random motion in the EIT calculation and the numerical results agree favorably with the experimental data. We also derive a set of effective parameters which are temperature dependent. This provides the understanding how the atomic motion affect the EIT medium quantitatively. Finally, we apply the aforementioned numerical method to the stationary light pulses (SLPs) based on the effect of EIT with counterpropagating laser fields and show how a SLP form in cold media. In the part of non-zero temperature BEC, we briefly discuss the properties of the stochastic projected Gross-Pitaevskii equation (SPGPE) for the Bose gases at non-zero temperature. Apply the SPGPE to spinor Bose condensate, we study the formation of the topological defects in rotating spin-1 Bose gas and spin-orbit coupled spin-1 Bose gas. Finally, we test the Kibble-Zurek scaling for the topological protected Josephson vortices in a linearly coupled Bose condensate. Our simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches,consistent with the Kibble-Zurek mechanism. However, slow quenches show stronger quench-time dependence that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime.