High Resolution Spectroscopy of Rydberg Excitons in External Fields

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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.