Bound States Of Trimers In A Strongly Resonant P-Wave Superfluid

With the rapid development of theory and experimental technology, studies on ultracold fermionic gases of atoms have attracted much interrest in the field of Bose-Einstein condensation (BEC). A Fermionic gas of atoms is very different from the electronic system in a solid. There exists only Zeeman effects in a Fermionic gas of atoms. But there exists no spin-orbit coupling because of the charge neutrality of atoms. Furthermore, the interaction of Fermionic atoms is short-ranged. A Fermionic gas of atoms has a simple structure and it does not have the complexity of a liquid (such as a low-temperature Fermionic'He liquid). In this sense, the studies of many-body effects are greatly simplied for a Fermionic gas of atoms. Therefore, the study of various properties of a Fermionic gas of atoms has become one of the most active research fields in BEC, among which the realization of the superfluid state of a Fermionic gas of atoms have attracted great attention. A strongly resonant p-wave superfluid has been realized experimentally with 40K atoms. In this thesis, the properties of the bound states of the Fermionic trimers in a strongly resonant p-wave superfluid are studied by using the scattering theory.In Chapter I, the background, experimental technology, and theoretical studies of Fermionic gases of atoms are briefly introduced, with the Feshbach resonance technology highlighted since the Feshbach resonance can be used to tune the interaction strength of Fermionic atoms. In Chapterâ…¡, the theoretical model for strongly resonant p-wave superfluids is introduced in the framework of Green's functions.Chapter III is the most important part of the thesis. The properties of the bound states of Fermionic trimers in a strongly resonant p-wave superfluid are studied by using the scattering theory. From the relation between the pole in the scattering matrix and the bound states of trimers, the equation for determining the bound states of trimers is obtained. After the equation is discretized, it is used to find the bound states of trimers. We have carefully examined the numerical accuracy of discretization in terms of the scattering matrix. In consideration that the scattering length among the atoms can be tuned through the Feshbach resonance, the dependence of the binding energies of bound states of trimers on the resonance strength has been studied. We have computed the energies of the ground state and various excited states for a wide range of the resonance strength. The results show that, as the resonance strength increases, more and more bound states of trimers appear and the absolute values of the binding energies increase.