In the year 2020, I finished my bachelor’s thesis in the group of Artur Widera at the University of Kaiserslautern. It is titled “Numerical simulations of the Gross-Pitaevskii-Equation in dynamic disorder potentials”. The Gross-Pitaevskii-Equation, GPE for short, is a nonlinear Schrödinger equation that describes the behavior of Bose-Einstein-Condensates produced in ultracold atoms experiments. I’ve implemented a well-known algorithm for solving this equation. With an efficient numerical solver at hand i investigated several fascinating phenomena:

#### Expansion of a BEC

Because of the nature of optical dipole traps, the generated BEC is highly elongated in one direction. The resulting shape is sometimes compared to a cigar. One of the classical experiments performed with a BEC is to study its expansion dynamic after switching off the trapping potential. During this expansion process the aspect ratio is inverted, which is as a characteristic of a superfluid.

#### Expansion of a disordered BEC

Recently quite some effort was put into studying disordered BECs. One possibility of generating a disordered BEC is by superimposing an optical speckle potential onto the usual trapping potential. Depending on the strength the disorder potential punches holes into the BEC. If such a disordered BEC is released, the expansion dynamics differ from the usual behavior. One reason for this is that holes serve as nucleation centers for vortices during the beginning of the expansion process as can be seen in the following animation:

#### Time evolution of a Soliton

Another striking phenomenon of BECS is the support of solitons due to the nonlinear nature of the GPE. Solitons are wave packets that propagate in space without being distorted.

#### Files

A more in-depth analysis of these phenomena can be found in my thesis:

Original German version

Translated English version

The GPE-Solver written by me can be found on GitHub:

GitHub-Link

A Zip-File with all animations is here:

Animations