Patterns in Interacting Quantum Gases
Typ
Examensarbete för kandidatexamen
Program
Publicerad
2021
Författare
Bekassy, Viktor
Heuts, Olivia
Lech, Alex
Lundqvist, Carin
Magnusson, Erik
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Quantum gas , Fermi gas , Fermions , Magic numbers , Pauli crystals , Separation energy , Perturbation theory