The Dynamics Of STG Gas

Nowadays, the great experimental and theoretical progress has been made in the development of One-Dimensional(1D) quantum gases. In the experiments, the lattice potential is created by retro-reflected laser beams which confining the atoms to an array of1D tubes. The interaction strength can be tuned via Feshbach resonance technique and then different quantum phases can be realized. Among them, super-Tonks-Girardeau (STG) gas, Tonks-Girardeau (TG) gas and Cluster state are typical. Theoretically the exactly solvable model and numerical simulation have been used to analyze different properties of ID quantum gas.In this thesis, we study the dynamics of two interacting bosons in a harmonic trap. By separating the Hamiltonian into a center-of-mass part and a relative motion part, we get the exact wave function and energy spectrum. A phase diagram is obtained for different interaction parameters. With the help of the exact wave function and energy spectrum, we study the dynamics of the system from TG gas to STG gas and Cluster state and analyze the realization and stability of the STG gas. By releasing the different quantum gas to free space we investigate the time evolution of the single particle density. Finally, we investigate the dynamics of the system initially prepared in a Schrodinger cat state.