- 學位論文
高次諧波之玻姆軌跡分析與貝氏優化超快圓偏振阿秒雷射之產生
Bohmian Trajectory Analysis of High-Order Harmonic Generation and Bayesian Optimal Control of the Ultrashort Circularly Polarized Attosecond Pulse Generation
摘要
高次諧波和超快阿秒脈衝的產生是在二十一世紀的超快科學和科技中一個重要的進展，利用這些技術能產生在阿秒尺度上的同調極紫外光雷射。在實驗上，應用這種光源，可以對原子分子系統中的超快電子運動進行即時的觀察。 在論文的第一部分，我們利用第一原理來研究近閾值高次諧波的產生的量子動力學，為了能找出在近閾值附近的電子運動狀態，我們應用了玻姆力學來研究氫原子和氬原子在強場雷射下的阿秒電子動力學。利用時變廣義擬譜法，我們能準確而又有效的解出時變薛丁格方程式和無自相互作用的時變密度泛函理論。我們發現主要貢獻於高原區域的高次諧波是短的玻姆軌跡，而在截止頻率附近，這些短軌跡的貢獻被抑制，使得在截止頻率前的高次諧波強度相對較弱。但在截止頻率前的數個高次諧波，強度又會稍微變大。這是因為這部分的高次諧波是由雷射的峰值游離電子所產生的。再者，較長的玻姆軌跡會以較低的能量回到核，所以這些軌跡主要貢獻於低閾值高次諧波的產生。我們的這些結果對高次諧波的產生以及合成阿秒雷射脈衝有一個更深的認識。 在過去十年，雖然已經對線性偏振的阿秒雷射脈衝在理論上和實驗上有很多的研究，但是產生圓偏振的研究相對較少。產生圓偏振的高次諧波和阿秒極紫外光雷射脈衝在科學和科技上有很多的應用。而到目前為止，在實驗上能造出來最快的孤立圓偏振阿秒脈衝為大約150阿秒。現在的挑戰是要尋找能製造更快的偏振阿秒雷射脈衝的方法。 在論文的第二部分，我們以第一原理模擬以及最佳化單一氦原子所產生的高次諧波光譜，用以製造53阿秒的圓偏振脈衝。透過貝葉斯優化，我們可以控制以及最佳化雙色偏振閘的雷射波形，使得所產生在高原區域的一系列高次諧波的相位是匹配的。這是能產生阿秒脈衝的重要條件。另外，為了找出產生這些高次諧波的物理機制，我們對電子的加速度作小波分析，再對比從半古典理論所求得的量子軌道的時間和能量，我們發現這些同調的高次諧波是由短軌道激發而來的。我們提出的這個方法很有潛力可以幫助實驗以產生孤立的超快圓偏振阿秒脈衝。 總結，我們通過第一原理，能準確的計算出在強場雷射作用下電子的玻姆軌道，這個新發展能讓我們對高次諧波有一個準確又清晰的物理圖像。另外，我們在量子最佳化控制上所得的成果，能夠推廣至各種新穎的化學和物理的量子最佳化控制問題上。我們對強場物理這個領域在理論和計算技術都提供了新的發展，也對其背後的物理原理有更深的認識。
並列摘要
The study of very high-order harmonic generation (HHG) and the generation of isolated ultrafast attosecond (as) (10−18 sec) pulses is one the most important advancement in ultrafast science and technology in the 21st century. It has enabled the generation of coherent extreme ultraviolet (XUV) source in the attosecond time scale, leading to the real-time experimental observation of ultrafast electron dynamics in atomic and molecular systems. In the first major part of this thesis, we present an ab initio study of the quantum dynamics of high-order harmonic generation (HHG) near the cutoff in intense laser fields. To uncover the subtle dynamical origin of the HHG near the cutoff, we extend the Bohmian mechanics (BM) approach for the treatment of attosecond electronic dynamics of H and Ar atoms in strong laser fields. The time-dependent Schrödinger equation and the self-interaction-free time-dependent density functional theory are numerically solved accurately and efficiently by means of the time-dependent generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian. We find that the most devoting trajectories calculated by the BM to the plateau harmonics are shorter traveling trajectories, but the contributions of the short trajectories near the cutoff are suppressed in HHG. As a result, the yields of those harmonics in the region near the cutoff are relatively weak. However, for the last few harmonics just above the cutoff, the HHG intensity becomes a little higher. This is because the HHG just above the cutoff arises from those electrons ionized near the peak of the laser pulse, where the ionization rate is the highest. In addition, the longer Bohmian trajectories return to the core with lower energies, these trajectories contribute to the below-threshold harmonics. Our results provide a deeper understanding of the generation of supercontinuum harmonic spectra and attosecond pulses via near cutoff HHG. While there are a number of experimental and theoretical studies on the generation of linearly polarized (LP) attosecond laser pulses in the past decade, the study of the generation of circularly polarized (CP) attosecond laser pulses is relatively new. The generation of CP HHG and attosecond XUV pules has significant numerous scientific and technological applications. To date, the world fastest and isolated CP attosecond pulse ever produced experimentally is around 150 as. A current challenge task is to explore the metrology for generating even faster CP attosecond pulses. In the second major part of this thesis, we present ab initio simulations of optimal control of high-order-harmonic generation spectra that enable the synthesis of a circularly polarized 53-attosecond pulse in a single Helium atom response. The Bayesian optimization is used to achieve control of a two-color polarization gating laser waveform such that a series of harmonics in the plateau region are phase-matched, which can be used for attosecond pulse synthesis. To find the underlying mechanisms for generating these harmonics, we perform a wavelet analysis for the induced dipole moment in acceleration form, and compare the time-energy representation with the quantum paths extracted from the semiclassical calculation. We found that these coherent harmonics are excited along the short trajectories. The proposed method has the potential to migrate to laboratories for generation of isolated circularly polarized ultrashort attosecond pulses. In conclusion, our new development of a fully ab initio 3D and accurate treatment of Bohmian trajectories to explore the laser-driven electron dynamics allows us to obtain an accurate and clear physical picture in HHG. Besides, our new development of the optimal control methods can be extended to the investigation of a broad range of quantum optimal control problems in novel chemical and physical processes of current interest. This thesis introduces the advancements in theoretical and computational techniques in the field of attosecond physics.