Patterns in Interacting Quantum Gases
Quantum gases is a novel field of experimental research, where it is possible to study the universal behaviour of quantum particles under controlled circumstances. In two experiments by Zürn et al. and Holten et al., patterns such as paring effects, magic numbers and Pauli crystals have emerged in a quantum gas consisting of a few ultracold 6Li atoms confined in an optical trap. By modelling these experiments and using the universal behaviour of quantum particles, we can achieve a greater understanding of how the building blocks of our universe behave and then apply that knowledge to more complicated systems, such as neutron stars or the atomic nucleus. This thesis aims to model the mentioned experiments as a few interacting fermions in a harmonic potential. By treating the interaction as a minor perturbation and calculating the energy of the system numerically with perturbation theory, we were able to compare our results with the experiments by Zürn et al. and found that they were in good agreement. Both showed a pronounced shell structure, resulting in magic numbers, and the emergence of pairing between fermions. Furthermore, the results were consistent with our analytically derived solution for two particles. Additionally, Pauli crystals in one and two dimensions were simulated using Matlab and the Metropolis algorithm, resulting in us successfully recreating the very recent experimental results by Holten et al.. Finally, interactions were added to Pauli crystals in 1D, showing new pairing patterns and opening up for further research.