冷原子中的合成規範場及自旋軌道耦合

Synthetic Gauge Field and Spin-orbit Coupling in Cold Atoms

鄭俊輝(Jun-Hui Zheng)

指導教授 ： 王道維

國立清華大學/理學院/物理學系/博士(2016年)

摘要

本論文，我將討論不同系統中自旋軌道耦合的效應：旋量玻色-愛因斯坦凝聚系統，雙層費米系統，以及二維拓撲絕緣體系統。在旋量玻色-愛因斯坦凝聚系統中，我將主要討論自旋軌道耦合和兩體相互作用的混合效應。運用絕熱近似，我系統的研究了在合成規範場中旋量玻色-愛因斯坦凝聚的基態，激發態以及相關的效應。在雙層費米系統中，我主要考慮自旋-層耦合及超流的效應。通過映射到有效模型，我證明了在零溫下，加入層之間帶有自旋翻轉的隧穿項，可以大大提高超導配對的臨界磁場。在二維拓撲絕緣體中，我主要研究Kane-Mele模型，并考慮在鋸齒形邊界上單顆磁性雜質的效應。我得到Kane-Mele模型譜以及波函數的解析解并討論了它的電輸運性質。進一步構造了一維有效模型來描述該系統。

關鍵字

冷原子 ； 合成規範場 ； 自旋軌道耦合 ； 拓撲絕緣體

並列摘要

In this thesis, I will discuss the effect of spin-orbit coupling in different systems: spinor Bose-Einstein Condensate (BEC) system, bilayer Fermionic system, and 2D topological insulator. In the spinor BEC system, I focus on the hybrid effect of spin-orbit coupling and two-body interaction. By using adiabatic approximation, I systematically investigate the ground state, elementary excitations and related effects of a BEC within a
synthetic vector potential. In the bilayer Fermionic system, I consider the effect of spin-layer
coupling and superfluidity. By mapping to an effective model, I demonstrate that at zero temperature
the critical value of the magnetic field for pairing can be significantly increased by including a spin-flip tunnelling between layers. In the 2D topological insulator, I focus on the Kane-Mele (KM) Hubbard model and consider the effect of a single spin-flip impurity at the Zigzag edge. I analytically obtain the spectra and wavefunction of the KM model and then discuss its electronic transport property. Furthermore, I develop a low energy effective 1D model to describe the system.

並列關鍵字

Cold atoms ； Synthetic gauge field ； Spin-orbit coupling ； Topological insulator

參考文獻

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