Superexchange Interaction Between Ultracold Bosonic Atoms In A Double Well

Since the realization of Bose-Einstein (BEC) condensed in alkali mental atoms rarefied gas in 1995, Bose-Einstein condensed as a new phenomenon of matter became the research focus of quantum optics and ultracold atom physics. BEC has important applications in quantum information and precision measurement field. Compared with the conventional solid state crystals, the ultracold atoms quantum crystals are are highly controllable and more perfect. We can modify the parameter optical lattices by changing the frequencies, intensities, and polarizations of the lasers that forming the lattices, or through changing the collisional of the ultracold atoms by magnetic Feshbach resonance.Based on ultracold bosonic atoms in a double well simple model, we calculate the relationship with spin structure factor and the density of the structure factor within the two-site Bose-Hubbard model. Spin structure factor shows the temperature dependence of the spin excitation, the density of the structure factor shows that the temperature dependence of the excitation density, the spin excitations are responses for superexchange interactions. So we can understand superexchange interaction in a double well better. The spin structure factor for positive frequencies reveals that the temperature effect is very obious. At zero temperature, at the low frequency the spin excitations survive, as the temperature rises,. As temperature increases, the occurrence probability of low-frequency spin excitation reduction, increase at high frequencies. We have also calculated the density structure factor and found that, in frequency space, where the spin excitations are strong, the density excitations are depleted, and vice versa. Therefore, the behavior of the density structure factor corroborates the results obtained from the spin structure factor.This paper is divided into four chapters. In Chapter Ⅰ, we introduce the research progress of ultracold atom physics, Bose-Einstein condensed, experimental methods on ultracold atoms and BCS-BEC crossover. In Chapter Ⅱ, we introduce double well model, Bose-Hubbard model and superexchange interaction briefly. In Chapter Ⅲ we calculate spin correspond and spin susceptibilities. In Chapter Ⅳ, we start from ultracold bosonic atoms in a double well, In terms of eigenstates and eigenvalues of the Hamiltonian within the two-site Bose-Hubbard model. In Chapter Ⅴ, we calculate the spin structure factor and discuss the temperature dependence of the spin structure factor. In Chapter Ⅵ, we calculate the density of the structure factor, compared the integrated density structure factor and the integrated spin structure factor. The density excitations are also responses for superexchange interactions. Therefore, the behavior of the density structure factor corroborates the results from the spin structure factor. So we can understand superexchange interaction in a double well better.