In this thesis, we analytically and numerically study quantized vortex states aswell as their dynamics in rotating Bose-Einstein condensate at extremely low tem-perature.We present an efficient method–gradient flow with discrete normalization tofind the stationary solutions of the Gross-Pitaevskii equation and coupled Gross-Pitaevskii equations. We give a mathematical justif...

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condens...

We account for the interaction of the Bose-condensed fraction with the normal phase in an effective dynamical equation such as the Gross-Pitaevskii equation. We show that the low-energy excitations can be treated as sound waves with speed dependent on the condensate density. This allows us to reduce the problem to the calculation of the determinant of the Laplace operator on a curved space and ...

We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapp...

We report the creation of a Bose-Einstein condensate using buffer-gas cooling, the first realization of Bose-Einstein condensation using a broadly general method which relies neither on laser cooling nor unique atom-surface properties. Metastable helium ((4)He*) is buffer-gas cooled, magnetically trapped, and evaporatively cooled to quantum degeneracy. 10(11) atoms are initially trapped, leadin...

We analyze coherent two-color photoassociation of a Bose-Einstein condensate, focusing on stimulated Raman adiabatic passage (STIRAP) in free-bound-bound transitions from atoms to molecules. This problem raises an interest because STIRAP has been predicted to be absent in the nondegenerate case [Javanainen and Mackie, Phys. Rev. A 58, R789 (1998)]. Nevertheless, we find that Bose stimulation en...

We present a theoretical model to describe the dynamics of Bose-Einstein condensates in anharmonic trapping potentials. To first approximation the center-of-mass motion is separated from the internal condensate dynamics and the problem is reduced to the well known scaling solutions for the Thomas-Fermi radii. We discuss the validity of this approach and analyze the model for an anharmonic waveg...

We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes dynamically unstable when the effective intersite tunneling becomes negative. We further show how controlling the sign of the tunneling can be used to manage ...

Bose-Einstein condensation (BEG) of atoms with attractive mteractions i:< profoundly different from BEC of atoms with repulsive interactions. \Ye describe expenments with Bose condensates of 'Li atoms ..•...hich are weakJy attracting at uJ· tralaw temperature. We measure the distribution of condensate occupation numbers occurring in the gas using a near-resonant optical probe to image the atom ...

Rayleigh scattering off a Bose-Einstein condensate was studied. Exposing an elongated condensate to a single off-resonant laser beam resulted in the observation of highly directional scattering of light and atoms. This collective light scattering is caused by the coherent center-of-mass motion of the atoms in the condensate. A directional beam of recoiling atoms was built up by matter wave ampl...