In systems of ultracold atoms,  the  quantum  Efimov  effect  can  appear where identical bosons form an infinite tower of bound trimer states in the resonant limit, at the bound dimer dissociation threshold. The most characteristic feature of this effect is that their energy spectrum obey a geometric scaling law, which is universal in the sense that it emerges irrespective of the nature of the two body forces. Using  a  model  potential,  constructed  to  resemble the two body interaction between alkali atoms,  which was  fine tuned to control the  scattering  length,  energy  eigenvalues  for  the  two-  and  threebody problem were calculated numerically. The results where  fitted  to  the analytic theory and the appearance of the first Efimov state was positioned at a scattering length of -9.23rvdW , which is in good  agreement  with  the universal value -9.2rvdW . / I system av ultrakalla atomer kan en kvanteffekt, kallad Efimoveffekt, uppkomma  där  identiska  bosoner  bildar  ett  oändligt  torn  av  bundna  trekroppstillstånd då spridningslängden går mot oändligheten, vid dissociationströskeln för en svagt bunden dimer.  Det mest utmärkande för denna effekt är att Efimovtillståndens energispektrum följer en geometrisk skalningslag, som är universell i den meningen att den framträder oberoende av hur atomernas parvisa växelverkan ser ut.  Med hjälp av en modellpotential som konstruerats för att efterlikna den parvisa växelverkan mellan två alkaliatomer finjusterades spridningslängden.  Energiegenvärdena för två- och tre-kropps problemen  beräknades  numeriskt  vid  olika  spridningslängder.   Resultaten jämfördes  med  den  analytiska  teorin  och  den  första  tre-kroppsresonansen uppkom  vid  spridningslängden  -9.23rvdW ,  vilket  överenstämmer  med  det experimentellt funna universella värdet -9.2rvdW .

Doctor of Philosophy / Department of Physics / Brett D. Esry / The Efimov effect plays a central role in few-body systems at ultracold temperature and has thus accelerated a lot of studies on its manifestation in the collisional stability of the quantum degenerate gases. Near broad Feshbach resonances, Efimov physics has been studied both theoretically and experimentally through the zero-energy scattering observables. We have extended the theoretical studies of Efimov physics to a much broader extent. In particular, we have investigated the three-body Efimov physics near narrow Feshbach resonances and have also identified the Efimov features beyond the zero temperature limit. We have found, near a narrow Feshbach resonance, the non-trivial contribution from both of the resonance width and the short-range physics to the three-body recombination and vibrational dimer relaxation. Remarkably, the collisional stability of the Feshbach molecules are found to be opposite to that near the broad resonances: an increased stability for molecules made by bosons and a decreased stability for those made by fermions. The universal physics observed near the narrow Feshbach resonances is further found not to be limited to the zero temperature observables. We have found that the general features of Efimov physics and those pertaining to a narrow resonance are manifested in different energy ranges above zero temperature. This opens the opportunity to observe Efimov physics by changing the collisional energy while keeping the atomic interaction fixed. The landscape of the universal Efimov physics is thus delineated in both of the interaction and the energy domain. We have also investigated Efimov physics in heteronuclear four-body systems where the complexity can be reduced by approximations. In particular, we have proposed ways for controllable production of the Efimov tri-atomic molecules by three-body or four-body recombinations involving four atoms. We have also confirmed the existence of four-body Efimov effect in a system of three heavy particles and one light particle, which has resolved a decade-long controversy on this topic. Finally, we have studied the collisional properties of four identical bosons in 1D, which is important to the experiments on the quantum gases confined in the 1D optical lattices.

Les gaz d'atomes ultrafroids offrent des possibilités sans précédent pour la réalisation et la manipulation des systèmes quantiques. Le contrôle exercé sur les interactions entre particules permet d'atteindre le régime de fortes interactions, pour des espèces d'atomes à la fois fermioniques et bosoniques. Dans la limite unitaire, où la force d'interaction est à son maximum, des propriétés universelles émergent. Pour les atomes bosoniques, celles-ci comprennent l'effet Efimov, l'existance surprenante d'une séquence infinie d'états liés à trois corps. Dans cette thèse, nous avons étudiés un système de bosons unitaires. Partant des cas à deux et à trois corps, nous avons montrés que le modèle choisi capturait correctement les caractéristiques universelles de l'effet Efimov. Pour le modèle à N-corps, nous avons développé un algorithme de Monte Carlo quantique capable de réaliser les différentes phases thermodynamiques du système : gaz normal à haute-température, condensat de Bose-Einstein, et liquide d'Efimov. Un unique composant de notre modèle resterait pertinent à la limite de température infinie, à savoir la répulsion corps dur à trois corps, qui constitue une généralisation du potentiel classique entre sphères dures. Pour ce modèle, nous avons proposé une solution au problème d'empilement compact en deux et trois dimensions, fondée sur une Ansatz analytique et sur la technique de recuit simulé. En étendant ces résultats à une situation de pression finie, nous avons montré que le système présente une transition de fusion discontinue, que nous avons identifié à travers la méthode de Monte Carlo. / Ultracold atomic gases offer unprecedented possibilities to realize and manipulate quantum systems. The control on interparticle interactions allows to reach the strongly-interacting regime, with both fermionic and bosonic atomic species. In the unitary limit, where the interaction strength is at its maximum, universal properties emerge. For bosonic atoms, these include the Efimov effect, the surprising existence of an infinite sequence of three-body bound states. In this thesis, we have studied a system of unitary bosons. Starting from the two- and three-body cases, we have shown that the chosen model correctly captures the universal features of the Efimov effect. For the corresponding many-body problem, we have developed a quantum Monte Carlo algorithm capable of realizing the different thermodynamic phases in which the system may exist: The high-temperature normal gas, Bose-Einstein condensate, and Efimov liquid. A single ingredient of our model would remain relevant in the infinite-temperature limit, namely the three-body hard-core repulsion, which constitutes a generalization of the classical hard-sphere potential. For this model, we have proposed a solution to the two- and three-dimensional packing problem, based on an analytical ansatz and on the simulated-annealing technique. Extending these results to finite pressure showed that the system has a discontinuous melting transition, which we identified through the Monte Carlo method.