Finite momentum condensate in spin-1/2 Bose gas with P-wave interaction and three-body problem in one dimension

Abstract

Due to its flexibility and controllability, ultracold atomic gases have become unique platforms for the investigation of few- and many-body physics. In particular, the most exciting opportunity offered by cold atom is that the interaction between particles can be changed by Feshbach resonance. So far, major achievements have been made for atoms with s-wave interaction. While on the other hand, the p-wave interaction between atoms has received comparatively much less attention. In this thesis, we investigate the properties of a spin-1/2 bosonic gas with attractive p-wave interactions and repulsive s-wave interactions. We propose a new ansatz for the wave function that describes the ground state of the system, which forms a spin singlet. We discuss the ground state energy and stability, as well as the excitation spectrum, which exhibits anisotropic behavior. We also investigate spin excitation and compare our ansatz with the traditional coherent state, finding that our ansatz is a much more natural candidate for the ground state. Furthermore, motivated by recent progress in creating fermion gas in one dimension with large effective range, we propose a p-wave two-channel model to describe the three-body scattering problem in the resonant limit, incorporating the effects of effective range. We derive the relevant STM equation to describe the three-body scattering and find an analytic three-body bound solution for special conditions. We also obtain general numerical solutions of the STM equation below the atom-dimer scattering threshold. We discuss the existence of the three-body bound states and its binding energy as a function of the two-body scattering length and the three-body coupling constant.