High-order terahertz sideband generation (HSG), recently discovered experimentally in semiconductors, is an extreme nonlinear optical phenomenon with physics similar to high-order harmonic generation (HHG) but in a much lower frequency regime. A key concept in understanding the HSG and HHG is the quantum trajectories, where the quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition of the Dirac-Feynmann path integral. However, in contrast to HHG in atoms and molecules, HSG in semiconductors can have interesting effects due to nontrivial “vacuum” states of band materials. A rich structure of the Bloch states in condensed matter systems would lead to a variety of phase effects in extreme nonlinear optics. / In this thesis, we show that in semiconductors with nontrivial gauge structures in the energy bands, the curved quantum trajectory of an electron-hole pair under a strong elliptically polarized terahertz field can accumulate a geometric phase. In particular, the geometric phase becomes the famous gauge invariant Berry phase for a cyclic trajectory. Taking monolayer MoS₂ as a model system, we show that the Berry phase appears as the Faraday rotation angle in the pulse emission from the material under short-pulse excitation. This finding reveals the Berry phase effect in the extreme nonlinear optics regime for the first time. / We further apply the Berry phase dependent quantum trajectory theory to biased bilayer graphene under strong elliptically polarized terahertz fields. The biased bilayer graphene with Bernal stacking has similar Bloch band features and optical properties to the monolayer MoS₂, such as the time-reversal related valleys and valley contrasting optical selection rule. However, the biased bilayer graphene has much larger Berry curvature than that in monolayer MoS₂, which leads to a large Berry phase of the quantum trajectory and in turn a giant Faraday rotation of the optical emission (∼ 1 rad for a THz field with frequency 1 THz and strength 8 kV/cm). This surprisingly big angle shows that the Faraday rotation can be induced more efficiently by the Berry curvature in momentum space than by the magnetic field in real space. It provides opportunities to use bilayer graphene and THz lasers for ultrafast electro-optical devices. / Finally, we study the geometric phase of a quantum wavepacket driven adiabatically along a trajectory in a parameterized state space. Inherent to quantum evolutions, the wavepacket can not only accumulate a quantum phase but may also experience dephasing, or quantum diffusion. We show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we again study the quantum trajectories of HSG in monolayer MoS₂. We find that while the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands which can be measured experimentally. The discovery of the geometric quantum diffusion extends the concept of geometric phases. / 最近，在實驗上發現了半導體中的一個極端非線性光學現象，即高次太赫茲邊帶產生(HSG)。它是原子与分子系统里的高次谐波产生(HHG)在太赫茲頻域的一個推广。HSG与HHG的關鍵物理過程均可用量子轨道理论解释，其中粒子的路徑積分描述的量子演化由若干滿足穩相近似條件的量子軌道主導。但是HHG与HSG之間存在着本質區別，即半導體的“真空態”可以具備一些非平凡的拓撲結構，從而給極端非線性光學领域帶來許多有趣的物理效應。 / 在這篇論文中，我們發現在強橢圓偏振太赫茲場作用下的具有非平凡规范結構的半導體中，電子空穴對的量子軌道可以積累一個非零的幾何相。特別地，如果我們考慮週期量子軌道，這個幾何相便成為著名的規範不變的Berry相。我們取單層MoS₂為模型系統，發現在光脉衝激勵下的材料中的光信號經歷一個法拉第旋轉，而且轉角由量子軌道的Berry相給出。這個發現首次揭示了極端非線性光學領域內的Berry相效應。 / 我們進一步將含Berry相效應的量子軌道理論應用于強橢圓偏振太赫茲場作用下的雙層石墨烯中。Bernal堆疊的雙層石墨烯与單層MoS₂具有某些相似的能帶結構与光學性質，例如兩者都具有兩個時間反演對稱的谷，且兩個谷內具有不同的躍遷選擇定則。但是雙層石墨烯有遠遠大於單層MoS₂的Berry曲率，從而其內的量子軌道也會積累一個遠遠大於單層MoS₂的Berry相。這個Berry相可以導致光信號巨大的法拉第旋轉（在頻率1THz以及場強8kV/cm的太赫茲場下約為1rad）。這個傳統方法下所無法產生的巨大法拉第旋轉說明比起實空間內的磁場，動量空間內的Berry曲率可以更加有效地誘發光信號的法拉第旋轉。我們的結果可以促使雙層石墨烯以及太赫茲激光在超快光電設備中的應用。 / 最後，我們考慮具有非平凡規範結構的參數空間內的量子波包在絕熱驅動下的量子演化。在演化過程中，這個波包不僅可以獲得一個量子相位，而且會經歷退相干（即量子擴散）。我們發現波包的一部分量子擴散具有幾何性質，而且這部分量子擴散可以表示為一個复幾何相的虛部。這個复幾何相可以通過量子軌道附近的帶有幾何相的量子路徑的相干來解釋。作為例子，我們研究了強橢圓偏振太赫茲場作用下的單層MoS₂中的量子軌道的复幾何相。我們發現此幾何相的實部誘發光的法拉第旋轉，而虛部則表現為邊帶光信號的橢圓偏振度，並且進而可以從實驗上進行測量。我們關於虛幾何相的研究拓展了幾何相這一概念的新領域。 / Yang, Fan = 強太赫茲場下半導體中的量子軌道的Berry相 / 楊帆. / Thesis Ph.D. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 71-75). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Yang, Fan = Qiang tai he zi chang xia ban dao ti zhong de liang zi gui dao de Berry xiang / Yang Fan. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1291261 |
| Date | January 2014 |
| Contributors | Yang, Fan (author.), Liu, Renbao (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Physics. (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (xiv, 82 leaves) : illustrations (some color), computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-NoDerivatives 4.0 International" License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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