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Identifier 000424023
Title Effect of the finiteness of the atom number on the superfluid properties of Bose-Einstein condensed gases
Alternative Title Φαινόμενα που σχετίζονται με τις υπέρρευστες ιδιότητες των συμπυκνωμάτων Bose-Einstein στην περίπτωση πεπερασμένου αριθμού σωματιδίων
Author Ρούσσου, Αλεξάνδρα
Thesis advisor Καβουλάκης, Γεώργιος
Εφραιμίδης, Νικόλαος
Abstract In the present thesis I have studied problems which are related to the behaviour of bosonic atoms at zero temperature and as a result they are Bose-Einstein condensed. Quite generally my thesis explores some of the effects which belong to the collection of phenomena that constitute “superfluidity”. In all my projects I have assumed one-dimensional motion of the atoms, and I have also imposed periodic boundary conditions, which is suitable for a ring potential. A substantial part of my thesis focuses on the corrections due to the finiteness of the atom number. These corrections come from correlations which show up beyond the mean-field approximation. The derived results are based mostly on the method of diagonalization of the many-body Hamiltonian, while I have also used the meanfield approximation. The novelty of my results relies on the combined effect of one-dimensional motion, the imposed periodic boundary conditions, and the small atom numbers that I considered. As shown below, all of these give rise to effects which have not been investigated so far. The experimental motivation for my studies comes from numerous experiments which have created and observed persistent currents in atomic Bose-Einstein condensates in topologically-nontrivial traps, i.e., annular and toroidal. In addition, the advances in atom detection has allowed experimentalists to lower the number of atoms and even work with just a few of them. In the first project of my thesis I investigated two questions. The first was the phenomenon of hysteresis, i.e., the hysteresis loop and the corresponding critical frequencies. The second question was the critical coupling for stability of persistent currents, paying particular attention to the effect of the finiteness of the atom number on it. In the second project of my thesis I studied the effect of the finiteness of the atom number on the solitary-wave solutions, going beyond the mean-field approximation. To attack this problem, I developed a general strategy, and considered a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that I extracted from the mean field approximation. The resulting many-body state has all the desired features and is lower in energy than the corresponding mean-field state. In the third project I studied the rotational properties of a two-component Bose- Einstein condensed gas of distinguishable atoms. I demonstrated that the angular momentum may be given to the system either via single-particle, or “collective" excitation. Finally, despite the complexity of this problem, under rather typical conditions the excitation spectrum has a remarkably simple and regular form.
Language English
Subject Atomic traps
Cold atoms
Finite number of atoms
Persistent currents
Rotational frequencies
Zero temperature
Μηδενική θερμοκρασία
Παγίδες ατόμων
Περιστροφικές ιδιότητες
Συμπηκνώματα Bose-Eiatein
Ψυχρά άτομα
Issue date 2019-07-26
Collection   Faculty/Department--Faculty of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Doctoral theses
  Type of Work--Doctoral theses
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