以第一原理含時密度泛函理論研究雙原子分子在超短強場雷射下的多光子效應及量子最佳控制理論

Abstract

我們以第一原理計算和研究雙原子分子在超短強場雷射下的多光子過程，並且使用了對遠距位能修正過的含時密度泛函理論 (time-dependent density functional theory) 來處理多電子分子系統。為了得到準確並有效率的結果，我們採用推廣到雙元子系統的廣義擬似譜法 (generalized pseudospectral method) 來做數值處理。在多光子電離的計算中，可發現分子軌域的排列方向會直接的影響不同軌域的電離順序。而我們也獲得詳細的高次諧波頻譜 (high harmonic generation) 及比較了最高電子佔有軌域做出的貢獻。我們還發現到一氧化碳分子帶有的永久電偶極矩破壞了反轉對稱，從而產生原子系統不會出現的偶數高次諧波。 另外在本篇論文中，我們用最佳控制理論 (optimal control theory) 成功的控制且達到在雙能階系統下的時變目標，並應用共軛梯度法 (conjugate gradient algorithm) 大幅減少數值迭代所需的次數。

We present an ab initio study of the time-dependent density-functional theory (TDDFT) with proper asymptotic long-range potential for nonperturbative treatment of multi-photon processes of diatomic molecules in strong laser field. For accurate and efficient treatment of the TDDFT equations, the generalized pseudospectral method (GPS) is extended to two-center molecules system. The procedure allows nonuniform and optimal spatial grid discretization of the Hamiltonian in prolate spheroidal coordinates and the time propagation using the split-operator technique in the energy representation. The multiphoton ionization and high-order harmonic generation (HHG) of diatomic molecules N2, CO, and O2 in intense short laser pulse fields are calculated in detail. We observe both the electronic binding energy and the orientation of the orbitals affect the ionization rate. In the analysis of HHG, the highest occupied molecular orbital (HOMO) has dominant contribution, but accurate results have to be obtained with all-electron study. The CO molecule has a small permanent dipole moment cause the different nonlinear optical response to homonuclear molecules such as generating both even and odd harmonics. We also practice the optimal control theory using time-dependent targets on the two-level system with use of the conjugate gradient algorithm, therefore greatly reducing the number of iterations to reach convergence.