氫原子之強場—力學藉由 synchrosqueezing transformation 的Floquet 分析

Abstract

儘管時頻表示在時間-頻率上有不確定的難度，仍然在科學與科技中不同的領域上廣泛的使用。最近提出了一個方法稱為synchrosqueezing transformation，可以同時得到時間和頻率上高的解析度。藉由這個方法，我們能分析Schr odinger equation 數值解所得的transition amplitude。以氫原子的高非線性激發為例，證明此方法的效能。當原子被強場雷射(800 nm)M照射時，會藉穿隧游離的機制而發生游離。近來，發現不光是游離態被填充，電子的激發態也是如此。這種高非線性的激發現象，被視為remote lasing 或雷射誘導降雨的關鍵機制。雖然說這很重要，但其中的激發機制仍不是很了解。此論文的目標是藉由synchrosqueezing 的方式解釋雷射激發的物理機制。 我們得到激發態之時transition amplitude 的時頻光譜，且藉由adiabatic/nonadiabatic Floquet 理論來分析。氫原子受雷射要遷的力學表示如下。

當雷射開啟，波函數沿著adiabatic Floquet state 傳遞，adiabatic Floquet state 平滑的連接於起始的eigenstate。 當雷射強度增加時，起始的Floquet state 分裂為數十個和光子相關的分佈。 在經過雷射強度最強的點附近時，起始的Floquet state 和平滑連接於n = 3 eigen state 的Floquet state (稱為n = 3-Floquet state) 交錯。 偶(奇)數角動量的eigen state 被偶(奇)數的光子分佈之Floquet state 填充。 由n = 3-Floquet state ，藉由nonadiabatic transition t 傳遞至最終的eigen state 所對應的Floquet state，決定了trannsition probability。 當偶(奇)數角動量的eigen state 靠近能量為偶(奇)數的光子分佈之(n = 3)- Floquet state 時，會有較大的transition 機率。

Time frequency representation is a useful technique commonly utilized in diverseelds of science and technology despite the diculty of the time-frequency uncertainty. Recently a method called the synchrosqueezing transformation has been proposed to achieve high resolution both in time and frequency. We use this method to analyze the transition amplitude obtained by solving the Schrodinger equation numerically. We take the highly nonlinear excitation of hydrogen as an example to demonstrate the usefulness of this method. When an intense laser eld (wavelength 800nm) irradiated to atoms, they are ionized through so called the tunneling ionization. Recently it is found that electronically excited states are populated as well as ionic states. This highly nonlinear excitation is understood as the key mechanism in remote lasing, or laser induced rain falling. Despite of its importance, the mechanism of excitation itself is not understood well. The purpose of this thesis is to elucidate the physical mechanism using the synchrosqueezing method. We obtained the time frequency spectra of the transition amplitude on excited states, and analyzed them using the adiabatic/nonadiabatic Floquet theory. The dynamics of the hydrogen excitation by intense laser eld is revealed as follows. As the laser is turned on, the wavefunction propagates along the adiabatic Floquet state that is smoothly connected with the initial eigen state (called the initial Floquet state). As the intensity increases, the initial Floquet state is splitted into many photon components. Around the laser peak the initial Floquet state crosses with one of the Floquet states that are smoothly connected to n = 3 eigen states (called the (n = 3)- Floquet state). An even (odd) l eigen state are populated as an even (odd) photon component in the (n = 3)-Floquet state. Nonadiabatic transition from the (n=3)-Floquet state to the Floquet state. converging to the nal eigen state determined the transition probability. An Even (odd) l state has large transition probability when the eigen energy is close to the energy of the even (odd) photon component of the (n = 3)-Floquet state.