High Resolution Spectroscopy of Rydberg Excitons in External Fields

本项目的主要目的在于系统地研究外场中里德伯激子的性质，特别强调半导体晶体环境的影响。首先，这将需要对外部场中的里德伯激子态和准朗道共振进行高精度光谱研究。这将包括对外部磁场和电场中的朗道梯和斯塔克梯的超激光光谱研究，这将使我们能够推导出里德堡激子的基本性质，如状态混合和它们的横向扩展。另一个主要的焦点将是在一个减少对称性系统中的量子混沌的统计处理，而不是微观处理。作为第一步，我们将研究里德伯激子的准朗道共振谱，预计它与氢的情况不同。由于构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，我们还将讨论水平间隔统计和对称在混沌中的作用。为此，我们将研究当外加电场、磁场或应变场降低系统对称性时的能级间隔统计量。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光传播方向的系统，并期望对系统的能级间隔统计以及进一步的扰动（如声子）的影响有深刻的见解。进一步，我们将研究电场和磁场联合作用下的里德伯激子，以寻找异常点。在这些点上，两个共振交叉，它们的能量和特征向量合并。这些只有在具有非厄米哈密顿量的系统中才能观察到，并且可能导致像无反射散射这样有趣的效应，并且可以通过在由电场和磁场跨越的二维参数空间中研究一个合适的圆来识别。最后，我们将研究弱外单轴应变场对里德伯激子的影响。这可能会导致里德伯激子能量的局部变化，因此可以用作标记，以便挑出晶体的小空间区域并将激子限制在其中。

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.