Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points

TL;DR

This paper introduces an improved iterative method to identify and analyze exceptional points in Rydberg systems under combined electric and magnetic fields, with potential experimental applications in solid-state systems.

Contribution

An innovative algorithm for locating exceptional points in quantum spectra and visualizing degenerate wave functions, applicable to both atomic and solid-state systems.

Findings

Existence of exceptional points in Rydberg systems confirmed.

High-field exceptional points are experimentally inaccessible in hydrogen.

Solid-state excitons offer feasible conditions for observing exceptional points.

Abstract

Exceptional points are special parameter points in spectra of open quantum systems, at which resonance energies degenerate and the associated eigenvectors coalesce. Typical examples are Rydberg systems in parallel electric and magnetic fields, for which we solve the Schr\"odinger equation in a complete basis to calculate the resonances and eigenvectors. Starting from an avoided crossing within the parameter-dependent spectra and using a two-dimensional matrix model, we develop an iterative algorithm to calculate the field strengths and resonance energies of exceptional points and to verify their basic properties. Additionally, we are able to visualise the wave functions of the degenerate states. We report the existence of various exceptional points. For the hydrogen atom these points are in an experimentally inaccessible regime of field strengths. However, excitons in cuprous oxide in parallel electric and magnetic fields, i. e., the corresponding hydrogen analogue in a solid state body, provide a suitable system, where the high-field regime can be reached at much smaller external fields and for which we propose an experiment to detect exceptional points.