強飛秒雷射致原子非線性激發之時頻分析

Abstract

即便測不準原理是難以克服的問題，時頻表象仍是一個有用的技術,並在科學與科技的各領域上有著廣泛的應用．近年來，同步擠壓轉換作為一個同時具有時間與頻率高解析的方法被發展出來。我們以氫原子的高非線性激發為例子，藉由分析從薛丁格方程式得到的躍遷振幅，並展示了同步擠壓方法的實用性。 當強雷射場（波長約為800奈米）照射到原子上，原子將經由被稱作穿隧游離的機制產生游離現象．然而近年來，人們發現，有時候也會產生電子被激發的情形，這種高非線性激發現象被認為是遠端雷射與人造雨的關鍵機制．然而雖然高非線性激發是那麼地重要，可是它的機制仍未被完全了解，而此論文的目的便是藉由同步擠壓方法來闡述其中物理機制。 我們利用絕熱與非絕熱弗洛赫理論來分析激發態的躍遷振幅之時頻圖．並揭露氫原子的強場激發機制如下： 考慮一初始位於1s態的氫原子，以一強場雷射照射，雷射強度一開始非常微弱，並隨著時間慢慢增強，我們發現原子被這樣逐漸增強的弱場所擾動後，其能量變化與基態之弗洛赫態相符並伴隨著些許的AC史塔克偏移。而當雷射強度足夠強的時候，有小機率會發生非絕熱躍遷至其他的弗洛赫態．這新的弗洛赫態是由其不同光子項與所有激發態所組成的。當雷射強度達到至高點並開始減弱，許多非絕熱躍遷發生，躍遷至其他激發弗洛赫態。最後當雷射關閉，它們會收斂至各個激發本徵態上。這樣收斂的過程中，奇角動量之能態會產生光子項的偏移，這種偏移現象在偶角動量能態上並未發生。2s和2p態為其中的例外，2s產生偏移，而2p卻沒有發生。 以上現象之機制，例如弗洛赫態的產生，弗洛赫本徵能量，多少光子項被包含，非絕熱躍遷的發生，以及弗洛赫態是如何的收斂到本徵態等，經由我們的時頻圖皆展現了出來。

Time frequency representation is a useful technique commonly utilized in diverse fields of science and technology despite the difficulty 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 field (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 in the hydrogen excitation by intense laser field is revealed as follows. The hydrogen atom initially on the 1s ground state is irradiated by a pulsed laser. In the beginning of the time, laser intensity is weak and gradually increasing. The atom is perturbed by this weak increasing field following the ground Floquet state with some AC stark shift. When the intensity is sufficiently strong, there is a nonadiabatic transition to another Floquet state with a small probability. This new Floquet state consists of all the excited eigen states with many different photon components. When the laser intensity decrease after the peak, there are other nonadiabatic transitions from the new Floquet state to many other excited Floquet states, which adiabatically converge to excited eigen states as the laser is turned off. In this converging process, a shift of photon number components takes place in the case of odd angular momentum states. This shift is not seen in even angular momentum states. The exceptions are in 2s and 2p states. 2s shows the shift, and 2p does not. It should be noted that our time frequency spectra clearly show all the above mechanisms, such as the population of Floquet states, Floquet eigen energies, how much photon components are included, when nonadiabatic transitions occur, how an Floquet state converges to an eigen state.