Exceptional points in the spectra of atoms in external fields

Abstract

We investigate exceptional points, which are branch point singularities of two resonance eigenstates, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedure to systematically search for exceptional points is presented, and their existence is proven. The properties of the branch point singularities are discussed with effective low-dimensional matrix models, their relation with avoided level crossings is analyzed, and their influence on dipole matrix elements and the photoionization cross section is investigated. Furthermore, the rare case of a connection between three resonances almost forming a triple-degeneracy in the form of a cubic root branch point is discussed.

12 pages, 9 figures, 1 table

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Cited by in corpus (27)

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• High-order exceptional points in optomechanics
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian
• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
• State Flip at Exceptional Points in Atomic Spectra
• Exceptional Points in three-dimensional Nanostructures
• Fingerprints of exceptional points in the survival probability of resonances in atomic spectra
• Non-adiabatic Modal Dynamics around Exceptional Points in an All-Lossy Dual-Mode Optical Waveguide: Towards Chirality Driven Asymmetric Mode-Conversion
• Time behaviour near to spectral singularities
• Topology of multipartite non-Hermitian one-dimensional systems
• Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Unconventional next nearest neighbor resonance coupling and states flipping mechanism in degenerate optical microcavities
• Parameter estimation in atomic spectroscopy using exceptional points
• Harmonic inversion analysis of exceptional points in resonance spectra
• Anomalous dynamical response of non-Hermitian topological phases
• A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides
• Classification of multiple arbitrary-order non-Hermitian singularities
• Rydberg excitons in electric and magnetic fields obtained with the complex-coordinate-rotation method
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Resonance scattering and singularities of the scattering function
• Realization of geometric phase topology induced by multiple exceptional points
• 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