Research On The Physical Properties Of Ultracold Atom System

Ultracold atom physics is an interdisciplinary subject that has been under exten-sive study in recent years. The progresses in the experimental techniques have greatly stimulated the developments of this direction. Important milestones in ultracold atoms include:trapping and cooling atoms using lasers in1985, the observation of Bose-Einstein condensation in1997, and the realization of degenerate Fermi gases etc. Due to the clean environment and highly tunable parameters, ultracold atoms has provided an idea platform for quantum simulation, i.e. implementing many-body Hamiltonians that are important in other branches of physics, e.g. condense matter physics, nuclear physics, etc.Based on the latest experimental progresses of the experiment, our research can be divided in to four parts. Firstly, we analyze the thermodynamic properties of attrac-tive Fermi gases using mean field theory. And this is motivated by the experiments of W.Ketterle’s group, where non-interacting atoms are cooled using gradient magnetic field by taking a similar setup. We show that the presence of interaction has dramatic impact on the cooling process, which makes it less efficient. Secondly, we study the stability of the topological superfluid phase in a trapped two-dimensional Fermi gas with spin-orbit coupling in a harmonic trapping potential. We systematically map out the phase diagram of the trapped gas, and find a shell structure of the different phases. We also propose a detection scheme for the topological superfluid phase. Due to the recent experimental realization of synthetic gauge field in ultracold atoms, our study has important implications for future experiments. Thirdly, we study the density and phases of a rotating Bose-Einstein condensate with spin orbit coupling. Although the non-interacting spinful bosonic systems is degenerate under spin orbit coupling, inter-action will lift the degeneracy and leads to rich physics. We systematically study the response of the system to rotation, and find interesting density distributions with dif-ferent parameters. Finally, we propose an experimental scheme for the preparation of the Dicke state in an N-particle spin chain. This has important applications in quantum information and quantum simulation.