量子力學在動量空間的表象及其在鋰原子的強場游離之應用

Abstract

我們建立了一套準確且有效率的方法，去解原子和雷射交互作用在動量空間的表象的薛丁格方程式。我們的方法是建立在分離運算子方法(split-operator method)和有限積分範圍的蘭迪方法(Landé subtraction method with finite integration limits)之上。我們測試了包含線性偏極脈衝、圓形偏極脈衝和長波長脈衝的情況，我們的計算結果和其他計算方法得到的結果是一致的。我們也用有限積分範圍的蘭迪方法去推廣李文斯坦模型(Lewenstein model)。接下來，我們應用已建立的動量空間薛丁格方程式解法，去做鋰原子的強場游離的研究。在較低雷射強度的區 域 ， 經由分析相關的束縛態被佔 據的歷史和將光電子頻譜(photoelectron spectra)分成奇數和偶數角動量部分，我們可以追溯出多光子游離(multiphoton ionization)在光電子頻譜形成的峰點的來源。在較強雷射強度的區域，我們指出了電子會穩定地停留在雷德堡態(Rydberg states)並解釋了為什麼游 離電子明顯集中到垂直於雷射偏極的方向。

We developed an accurate as well as efficient scheme to solve time-dependent Schrödinger equation in momentum space of an atom interacting with a laser pulse. Our scheme is based on split-operator method in energy representation and Landé subtraction method with finite integration limits. Cases of linearly polarized pulse, circularly polarized pulse, and long wavelength pulses are tested. Our results agree well with those from coordinate space calculations. We also apply the Landé subtraction method with finite integration limits to generalize Lewenstein model. Next, we use the developed P-space TDSE to study the strong-field ionization of a lithium atom with a linearly polarized pulse. By analyzing the population history of relevant bound states and separation the photoelectron spectra into odd and even angular momentum parts, we can trace the origin of multiphoton ionization peaks in the lower intensity regime. We point out the Rydberg stabilization and explain why the fan structure becomes evident in the direction perpendicular to the polarization axis in the higher intensity regime.