Quantum Problems In The Super-Cold Atoms And The System Of Molecules In Intense Laser Field

Bose-Einstein condensates(BECs) trapped in external potential and molecular in intense laser field are two typical complex systems,which are governed by nonlinear interaction.The quantum problem in these two systems,especially induced by their nonlinear interactions,is the current hot point both in the theoretic and experimental view.In this thesis,we investigated the bifurcation of the stationary solutions,nonlinear dynamics of BECs with double potential and the non-sequence double ionization(NSDI) of molecular in intense laser field.The main results are as following:Based on the analytical solutions for BECs with double square well,we introduced one analytical approximation method to study the bifurcation of its stationary solutions.And after carefully calculating the relative parameters in Bose Josephson Junction Model,we introduced one new tunneling concept: nonlinear tunneling and some nonlinear corrections to the BJJ model have been presented.It has been shown that there are symmetry breaking(or non linear corresponding) stationary solutions for BECs with double well potential when the nonlinear interactions are larger than some critical values.Further more,these symmetry breaking stationary solutions are bifurcated from the symmetry keeping solutions.In the case of the weak nonlinear interaction, we introduced one analytical approximation method to find the stationary solutions for nonlinear Schr(o|¨)dinger equation(Gross-Pitaevskii equation) with double square well by linear stationary solutions of Schr(o|¨)dinger equation. The critical nonlinear parameters,over which the symmetry breaking solution can be exist,can be exactly predicted from our method.And we can also find the nonlinear stationary solutions are in good agreement with the analytical results,in relative larger range of the nonlinear parameters(|η|＜40) by our approximation method.After carefully calculating the parameters in BJJ model,we find that one novel tunneling effect,nonlinear tunneling effect,has to be considered in the case of larger nonlinear interaction parameters.This effect can be understood as a particle tunneling through the nonlinear effective potential(η|Φ_1,2|²) and can't exsit in the linear case.This nonlinear tunneling effect will bring an important correction to the system parameters,in the case of strong nonlinear interaction,for example,energy splitting due to tunneling,nonlinear critical values of macroscopic quantum self-trapping.Finally,we have extended the S-matrix method to study the NSDI of diatomic molecular in intense laser field.We found that the structure of the molecule plays an important role during the NSDI process:bonding 3σ_g highest occupied molecular ortital for N₂ does not affect the rate of NSDI while the antiboding 1Ï€_g structure for O₂ makes an obvious suppression effect on the rates of NSDI.Our results are qualitatively consistent with the experimental data.