Rydberg systems in parallel electric and magnetic fields: an improved method for finding 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 Schrödinger 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.

22 pages, 7 figures. Some improvements and one additional figure. Accepted for publication in J. Phys. B

References in corpus (13)

• Visualization of Branch Points in PT-Symmetric Waveguides
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Giant Rydberg Excitons in Cuprous Oxide
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Exceptional Points in Atomic Spectra
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Observation of high angular momentum excitons in cuprous oxide
• Impact of the valence band structure of Cu${}_2$O on excitonic spectra
• Exceptional points in the spectra of atoms in external fields
• State Flip at Exceptional Points in Atomic Spectra
• Linewidths in excitonic absorption spectra of cuprous oxide
• Signatures of the classical transition state in atomic quantum spectra
• Classical dynamics and localization of resonances in the high energy region of the hydrogen atom in crossed fields

Cited by in corpus (19)

• Exceptional points and the topology of quantum many-body spectra
• The even exciton series in Cu${}_2$O
• Magnetoexcitons in cuprous oxide
• Interaction of Rydberg Excitons in Cuprous Oxide with Phonons and Photons: Optical Linewidth and Polariton Effect
• Electrooptical Properties of Rydberg Excitons
• Magnetooptical Properties of Rydberg Excitons - Center-of-Mass Quantization Approach
• Magnetoexcitons break antiunitary symmetries
• GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons
• Exciton-polaritons in cuprous oxide: Theory and comparison with experiment
• Influence of electron-hole plasma on Rydberg excitons in cuprous oxide
• Exceptional points in dielectric spheroid
• $K$ dependent exchange interaction of the $1S$ ortho exciton in Cu${}_2$O
• Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics
• A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides
• Rydberg excitons in electric and magnetic fields obtained with the complex-coordinate-rotation method
• Exciton-phonon interaction breaking all antiunitary symmetries in external magnetic fields
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
• Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra
• Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points