High Resolution Spectroscopy of Rydberg Excitons in External Fields

该项目的主要目标是系统地研究里德堡激子在外场中的性质，特别是半导体晶体环境的影响。首先，这将需要对外场中的里德堡激子态和准朗道共振进行高精度的光谱研究。这将包括对朗道和斯塔克阶梯在外部磁场和电场中的超箭激光光谱学研究，这将使我们能够推导出里德堡激子的基本性质，如态混合及其横向扩展。另一个主要焦点将是通过统计而不是微观处理来讨论对称性约化系统中的量子混沌这一主题。作为第一步，我们将研究里德堡激子的准朗道共振谱，这有望不同于氢的情况。由于组成激子的电子和空穴的质量相似，我们期望对周期轨道有更深入的了解。除了周期轨道，我们还将讨论能级间距统计和对称性对混沌的作用。为此，我们将研究在外加电场、磁场或应变场的作用下系统对称性降低时的能级间距统计。利用晶体取向和光传播方向的不同组合，我们将能够研究高对称性和低对称性的系统，并有望深入了解系统的能级间距统计以及声子等进一步微扰的影响。此外，我们将研究电场和磁场组合中的里德堡激子，以寻找例外点。在这些点上，两个共振交叉，它们的能量和本征向量结合在一起。只有在具有非厄米哈密顿量的系统中才能观察到它们，并且可能导致像无反射散射这样的干涉效应，并且可以通过研究电场和磁场跨越的二维参数空间中的合适的圆来识别它们。最后，我们将研究弱的外部单轴应变场对里德堡激子的影响。这可能导致里德堡激子能量的局部变化，因此可以用作标记，以便挑选出晶体的小空间区域并限制其中的激子。

The main objective of the proposed project lies in a systematic investigation of the properties of Rydberg excitons in external fields with special emphasis on the effects of the semiconductor crystal environment. First, this will require high-precision spectroscopic studies of Rydberg exciton states and quasi-Landau resonances in external fields. This will include ultranarrow laser spectroscopy studies of the Landau and Stark ladders in external magnetic and electric fields, which will allow us to derive basic properties of Rydberg excitons such as state mixing and their lateral extension. Another main focus will be on the topic of quantum chaos in a system of reduced symmetry in terms of a statistical instead of microscopic treatment. As a first step, we will investigate the quasi-Landau resonance spectrum of Rydberg excitons, which is expected to differ from the case of hydrogen. Due to the similar masses of the electron and hole which consitute the exciton, we expect to develop a deeper insight into periodic orbits.Apart from periodic orbits, we will also address the question of level spacing statistics and the role of symmetry on chaos. To this end, we will investigate the level spacing statistics when the symmetry of the system is reduced by means of external electric, magnetic or strain fields. Using different combinations of crystal orientation and light propagation direction, we will be able to study systems of high and low symmetry and expect profound insights into the level spacing statistics of the system as well as the influence of further perturbations such as phonons.Further, we will investigate Rydberg excitons in combined electric and magnetic fields in order to find exceptional points. At those points two resonances cross and both their energies and eigenvectors coalesce. These are only observable in systems with a non-Hermitian Hamiltonian and may result in intrguing effects like reflectionless scattering and can be identified by investigating a suitable circle in the twodimensional parameter space spanned by the electric and magnetic fields.Finally, we will investigate the influence of weak external uniaxial strain fields on Rydberg excitons. These may result in a local variation of the Rydberg exciton energy and therefore may be used as a marker in order to single out small spatial regions of the crystal and confine excitons within them.