Funnel Potential Super-cold Boson Dynamic Behavior Of The Fermi Research

Bose-Einstein condensation (BEC) is a phenomenon related to many fields in physics. It is very important not only for basic theoretical research but also for the promising applications in techniques. Since BEC was realized in experiments, it has become an investigated platform for various effects of quantum many-body interaction in strongly correlated systems and has stimulated many new research fields. In 2004, Tonks-Girardeau gas was firstly achieved experimentally. It has attracted many researchers'attentions and has turned into a hot topic in recent physics field. It has also promoted the research of quantum information, quantum calculation and quantum coherence, as well as the research of strong correlated phenomena.So far, the researches of TG regime have been focused on the homogeneous ultracold Bose gas, external trapped potential are mainly harmonic oscillator potential and optical lattice potential, which have relatively matured in theory and experiment. However, the fermionization of inhomogeneous ultrcold Bose gas is not nearly studied. In this paper, we propose an inhomogeneous funnel potential, and ultracold Bose gas is loaded in funnel potential. We apply the variational method to study the dynamical features and conditions of fermionized Bose gas.The thesis is consisted of four chapters. Chapter one is briefly an introduction of the novel quantum state-TG gas and its theory model and its experimental research. In chapter two, we mainly introduce the nature of ultracold Bose gas in the harmonic oscillator potential and optical lattice potential theoretically and experimentally. In chapter three, we study the nature of ultracold Bose gas in the funnel potential through variational method. The results show that as aspect ratio increases, the longitudinal density has changed interestingly in funnel potential, and ultracold Bose gas experiences the process of fermionization. Compared with highly elongated harmonic potential, it is easier to realize crossover from the three-dimensional regime to the one-dimensional regime for ultracold Bose gas in funnel potential. Ultracold Bose gas enter the TG region in funnel potential, the peaks of momentum distribution become sharper with the number of atoms increasing. Besides, starting from the three-dimension Gross-Pitaevskii equation, we found out the one-dimensional nonlinear Schr?dinger equation, which can describe dynamic of ultracold Bose gas in the funnel potential. Finally, we discuss the feasibility that fermionization of ultracold Bose gas in funnel potential can be realized experimentally. The conclusions of this paper can provide a theoretical basis for the experimental realization. In chapter four, we make a summary of our work and some possible researches for future in this field.