Research Numerically The Macroscopic Quantum Properties Of BEC By The SSCN Method

Bose-Einstein Condensation (BEC) has become a hot spot of physics research after its realization in dilute atomic gas quickly. The macroscopic properties study of BEC in harmonic or optical lattice trap are two important aspects, and it has achieved remarkable success between theoretical and experimental work. In theory the dynamic properties of BEC are mainly by solving the mean-field Gross-Pitaevskii equation (G-P equation). It is difficult to acquire the precise solution of G-P equation because of the nonlinear term. So approximate or direct numerical methods are used usually. The Split-step Crank-Nicholson method (SSCN method) is a very efficient and stable algorithm among lots of numerical methods. It has obvious advantages especially when the nonlinear coefficient C is large or the iterative time is long. So the SSCN method is very suitable for numerical researching of BEC.At first, the macroscopic properties of BEC in harmonic trap is studied numerically in this paper using the SSCN method. One obtain the density distribution function of the evolution over time for a BEC when the magnetic trap is switched off or, is still hold on. The effect between the nonlinear coefficient C and the density distribution is discussed. Then we development the study into two BEC in double well. The interference evolution with time of two BEC when the trap is switched off are simulated numerically. When the trap is still hold on, the density distribution shows the periodic oscillation and overlap. The overlap is consistent with the superposition principle of wave. At last, we take the optical lattices as a research model, the G-P equation in the combined potential which is comprised of optical lattices and harmonic potential is solved by the SSCN method, the time evolution of BEC in 1D and 2D optical lattices are simulated numerically, and the evolution properties with C=1and C=5 is contrastive studied. The ground state function of BEC with vortex in optical lattice is also discussed as a extension study of our topic. And it is the important work for us to study its macroscopic properties of time evolution by the SSCN method.