Quantum Dynamics Of Bose Gas At Low Temperature

In 1924, S. N. Bose wrote a paper on the statistics of photons. Following thiswork, A. Einstein considered a gas of non-interacting atoms and concluded thata macroscopic fraction of the total atoms will occupy the lowest-energy single-particle state below a certain critical temperature. In the following seventy years,Bose-Einstein condensation becomes one of the most exciting fields in modernphysics. Many famous physicists have contributed to this field. The list of thenames includes, for example, A. Einstein, F. London and his brother H. Lon-don, L. D. Landau, N. N. Bogoliubov, R. P. Feynman... ... The most importantadvancement of experiment happened in 1995. Three individual groups in USAgenerated almost purified Bose condensates of dilute alkalis gases in harmonictraps. By adjusting the frequencies of external traps, one- and two-dimensionBose condensates are generated too. Other important and interest experimen-tal results include the interference between two independent condensates, thesuper?uid-insulator transition of Bose gas in optical lattice, dark and brightsolitons in the condensates and tuning the interaction strength of atoms withFeshbach resonance,and so on. The breakthrough on the theory of Bose-Einsteincondensation started from the combination of condensates and macroscopic wavefunction. It is convenient and promotes the development of theory of condensates.Nowadays, it becomes one of the important tools on analyzing the condensates.On the other hand, quantum correlation e?ects plays an unique role in the studyof condensates, which in?uences the ground state and dynamics of the systemeven at almost zero temperature. In this thesis, we study the many-body dy-namics of finite Bose gas at low temperature. The work concentrates on thequantum dynamics of one dimensional Bose gas with attractive interaction andthe entanglement of two-component Bose condensates in a double-well.1. We investigate the many-body dynamics of an e?ectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theorypredicts that a bright-soliton state will be formed when the interparticle inter- action increases over a critical point. The chemical potential is continuous whilethe first order derivation of the chemical potential is discontinuous. Thus thereis a quantum phase transition at the critical point. Due to the strong interac-tion strength of atoms in a soliton, quantum correlation has to be considered.The study of quantum many-body dynamics in this thesis reveals that thereis a modulation instability in a finite Bose system correspondingly. We showthat Shannon entropy becomes irregular near and above the critical point due toquantum correlations. We also study the dynamical behavior of the instabilityby exploring the momentum distribution and the fringe visibility, which can beverified experimentally by releasing the trap.2. We consider a novel system of two-component atomic Bose–Einsteincondensate in a double-well potential. Based on the well-known two-mode ap-proximation, we demonstrate that there are obvious avoided level crossings whenboth interspecies and intraspecies interactions of two species are increased. Thequantum dynamics of the system exhibits revised oscillating behaviors comparedwith a single component condensate. We also examine the entanglement of twospecies. Our numerical calculations show that the onset of paired-tunneling canbe signalled by a violation of the Cauchy–Schwarz inequality of a second-ordercross-correlation function. Consequently, we use Von Neumann entropy to quan-tify the degree of entanglement.