Effects of the dipole-dipole interaction on the physics of ultracold quantum gases

Abstract

In this thesis we study the effects of the dipole-dipole interaction on the physics of ultracold quantum gases, both bosonic and fermionic, within the theoretical framework provided by the mean-field regime. This kind of interaction takes place in ultracold atomic gases (for instance 52Cr or 164Dy) due to their atomic magnetic dipole moment, and in ultracold molecular gases due to the magnetic or electric dipole moment.

In the case of quantum gases of bosonic atoms, or Bose-Einstein condensates, the dipole-dipole interaction can be studied within mean-field approximation using the Gross-Pitaevskii equation, which now contains a new non-linear term due to the dipole-dipole interaction. We investigate, on the one hand dipolar condensates confined in harmonic traps, and on the other dipolar condensates confined in toroidal traps. In the harmonic geometry, our focus is on the study of the ground state and the quantized vortex state, where the density profile is characterized as well as some properties leading to the process of vortex formation, such as the critical frequency and the energy barrier that has to be overcome to bring the vortex from the surface to the centre of the gas. We finish the study of dipolar condensates in harmonic traps by dynamically simulating the precession frequency of an off-center vortex in a non-rotating condensate.

In the toroidal geometry the dipolar effects are strongly magnified when the polarization axis of the dipoles is perpendicular to the trap symmetry axis. In this case, the anisotropic structure of the density can be understood as the response of the system to the double-well effective potential along the ring. We have studied the dynamics of this system when the initial number of atoms in the left and right wells is imbalanced, predicting Josephson and self-trapping oscillations depending on the initial condition. This has led us to name this new system as Self-induced Josephson Junction. We have studied in detail the self-trapping regime and we have seen that the particle flux inversion is closely related to the crossing of vortices across the Josephson junctions. This result opens the door to establishing a more direct connection between the phase-slip regime, widely addressed in superfluid helium, and the self-trapping regime of condensates.

In the case of quantum gases of fermionic dipolar particles, we have studied how the radial quadrupole mode allows one to distinguish between hydrodynamic and collisionless regimes. We have analytically calculated the frequency of this mode in the mean-field approximation, generalizing the results from the Thomas-Fermi approximation for trapped ideal Fermi gases. On the one hand, we observe that the frequency in the hydrodynamic regime is smaller than in non-dipolar Fermi gases, while in the collisionless regime the frequency is larger or smaller than that corresponding to the non-interacting system depending on the geometry of the harmonic trap. On the other hand, we predict that reducing the trap deformation (aspect ratio) an observable jump in the frequency of the radial quadrupole mode would take place, which would correspond to the transition between the collisionless and hydrodynamic regimes, for instance when the gas undergoes the transition to the superfluid state.

En aquesta tesi s’estudien els efectes de la interacció dipol-dipol en la física dels gasos qu`antics ultrafreds, tant de caràcter bosònic com fermiònic, i dins del marc teòric del règim de camp mig. En el primer cas considerem condensats de Bose-Einstein dipolars confinats tant en trampes harmòniques com toroidals, descrivint-ne la geometria de l’estat fonamental i de l’estat de vòrtex quantitzat.En la geometria toroidal els efectes dipolars es veuen fortament magnificats quan l’eix de polarització dels dipols és perpendicular a l’eix de simetria de la trampa. Aquesta configuració ens permet introduïr el concepte de Junció de Josephson Autoinduïda (Self-induced Josephson Junction), en la qual hem predit oscil•lacions de Josephson i d’autoatrapament (self-trapping) depenent de la condició inicial. Estudiant en detall el règim d’autoatrapament hem vist que la inversió del flux de partícules està fortament lligada al creuament de vòrtexs quantitzats a travès de les unions de Josephson. Aquest resultat obre les portes a establir una relació més directa entre el règim dinàmic de salts de fase (phaseslips), àmpliament estudiat en heli superfluid, i el règim d’autoatrapament propi dels condensats. Finalment, en el cas de gasos quàntics de partícules dipolars fermiòniques, hem estudiat com les excitacions col•lectives, en concret el mode quadrupolar radial, permeten distingir entre els règims hidrodinàmic (que pot ser tant degut a la rapidesa de les interaccions com a la superfluidesa) i nocol•lisional (que té lloc quan les interaccions són a tan baixa freqüència que efectivament es poden negligir).