Ultracold collisions in traps

The ultracold atomic and molecular physics as it is accessible, e. g. , in Bose-Einstein condensates of dilute gases was investigated. In such systems two-body collisions are dominant and their detailed study is one of the central topics of this work. They were done considering elementary chemical reactions as photoassociation, and magnetic Feshbach resonances. Additionally, studies of atoms in optical lattice sites were carried out. The many-body systems were not only considered within the usually adopted mean-field approach but also beyond that in order to simulate the fully correlated motion. A collision of two particles is in general a multi-channel problem. However, in many cases it cannot be treated completely for practical reasons. In order to overcome this problem the single-channel schemes are usually adopted. A number of effective single-channel schemes were developed in this work in order to approximate such collisions. The applicability of these schemes was verified comparing to multi-channel solutions in the presence of a resonant magnetic field. An interesting aspect in ultracold physics is that atoms can bind together to form ultracold and even Bose-Einstein condensed molecules. Molecules may be achieved by, e. g. , Feshbach resonances or photoassociation. In this work the influence of a tight isotropic harmonic trap on photoassociation of two ultracold atoms forming a homonuclear dimer was investigated. To this end, different photoassociation schemes were considered with respect to their experimental realizability and their possible manipulation by external confinement. For the first time, realistic molecular potentials were consistently accounted for in the photoassociation problem in a trap. An important progress in physics at ultracold energies was the loading of the ultracold gas into an optical periodic lattice formed with the aid of standing light waves. In this work, a theoretical approach was developed that allows for a full numerical description of an atomic pair trapped in a threedimensional optical lattice. This approach includes the possible coupling between center-of-mass and relative motion coordinates in a configurationinteraction manner and uses realistic interatomic potentials. The developed method was applied to model experimental data, where radio-frequency association was used to create molecules from fermionic and bosonic atoms in a three dimensional cubic optical lattice. A very recent application of this approach allowed to compare the Bose-Hubbard model which is frequently used in solid state physics with the exact solution for different multi-well lattices. The applicability range of the Bose-Hubbard model was examined and corrections were determined. An exact treatment of polar molecules in traps, atom-ion collisions, quantum dots, atoms in effective one and two dimensional geometries, systems in double-well and triple-well potentials become possible within the framework of the developed theory with minor extensions. The dynamic properties involving the solution of the time-dependent Schrödinger equation can also be accounted for straightforwardly. For simulating the fully correlated motion in ultracold many-body systems a B-spline based configuration-interaction approach was developed. In this approach the two-body interparticle interaction was described by the pseudopotential. It turned out that with this choice of the two-body model potential the presently developed many-body approach does not converge. The reasons are not yet fully explained in literature. The two-body studies done in this work should be a good basis to understand the consequences of applied approximations as well as for further many-body research.