论文标题
几何阶段及其应用：拓扑阶段，量子步行和非惯性量子系统
Geometric phase and its applications: topological phases, quantum walks and non-inertial quantum systems
论文作者
论文摘要
几何阶段在量子理论中起着基本作用，并且说明了广泛的现象，从aharanov-bohm效应，整数和分数量子厅效应以及物质的拓扑阶段，包括拓扑绝缘子，等等。在本论文中，我们提出了一个新的大地测量和空相曲线的视角，这是理解几何阶段的关键要素。我们还研究了在拓扑阶段，量子步行和非惯性量子系统中几何阶段的许多应用。 给定表面上任意两个点之间的最短曲线是（最小）测量。它们也是系统无法获得任何几何阶段的曲线。在同一情况下，我们可以概括地测量学以定义更大类的曲线，称为无效相位曲线（NPC），而所获得的几何相也为零。但是，它们不必是两个点之间的最短曲线。我们已经提出了在Bloch球体上的几何分解和无效的相位曲线，这对于提高我们对状态空间的几何形状以及地理位学和NPC的内在对称性至关重要。 在存在外部（有损）环境的情况下，我们还研究了量子步行中拓扑阶段的持久性。我们表明，一维量子行走中的拓扑顺序持续到适度的损失。此外，我们使用几何阶段来检测通过放置在空腔内的圆形旋转的两级原子感知到的场相关因子的非惯性修饰。
Geometric phase plays a fundamental role in quantum theory and accounts for wide phenomena ranging from the Aharanov-Bohm effect, the integer and fractional quantum hall effects, and topological phases of matter, including topological insulators, to name a few. In this thesis, we have proposed a fresh perspective of geodesics and null phase curves, which are key ingredients in understanding the geometric phase. We have also looked at a number of applications of geometric phases in topological phases, quantum walks, and non-inertial quantum systems. The shortest curve between any two points on a given surface is a (minimal) geodesic. They are also the curves along which a system does not acquire any geometric phase. In the same context, we can generalize geodesics to define a larger class of curves, known as null phase curves (NPCs), along which also the acquired geometric phase is zero; however, they need not be the shortest curves between the two points. We have proposed a geometrical decomposition of geodesics and null phase curves on the Bloch sphere, which is crucial in improving our understanding of the geometry of the state space and the intrinsic symmetries of geodesics and NPCs. We have also investigated the persistence of topological phases in quantum walks in the presence of an external (lossy) environment. We show that the topological order in one and two-dimensional quantum walks persist against moderate losses. Further, we use the geometric phase to detect the non-inertial modifications to the field correlators perceived by a circularly rotating two-level atom placed inside a cavity.
