Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra

Abstract

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in particular in systems, where the computation of the quantum spectra and resonances is numerically very expensive. We introduce an efficient machine learning algorithm to find exceptional points based on Gaussian process regression (GPR). The GPR-model is trained with an initial set of eigenvalue pairs belonging to an EP and used for a first estimation of the EP position via a numerically cheap root search. The estimate is then improved iteratively by adding selected exact eigenvalue pairs as training points to the GPR-model. The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system, viz., the localization of EPs in the resonance spectra of excitons in cuprous oxide in external electric and magnetic fields. The precise computation of EPs, by taking into account the complete valence band structure and central-cell corrections of the crystal, can be the basis for the experimental observation of EPs in this system.

arXiv comment28 pages, 10 figures, submitted to Machine Learning: Science and Technology

References in corpus (22)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• PT-Symmetric Quantum Mechanics
• Repulsion of Resonance States and Exceptional Points
• Giant Rydberg Excitons in Cuprous Oxide
• An Intuitive Tutorial to Gaussian Process Regression
• Observation of Exceptional Points in Electronic Circuits
• Exceptional Points in Atomic Spectra
• Non-Hermitian engineering of terahertz light using exceptional points in electrically tuneable collective light-matter interactions
• Chirality of wave functions for three coalescing levels
• Observation of high angular momentum excitons in cuprous oxide
• Fine structure of excitons in Cu${}_2$O
• Deviations of the exciton level spectrum in cuprous oxide from the hydrogen series
• Coulomb-Sturmian basis for the nuclear many-body problem
• Impact of the valence band structure of Cu${}_2$O on excitonic spectra
• The even exciton series in Cu${}_2$O
• Exceptional points in the spectra of atoms in external fields
• Magnetoexcitons in cuprous oxide
• Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points
• Green exciton series in cuprous oxide
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Rydberg excitons in electric and magnetic fields obtained with the complex-coordinate-rotation method
• Interseries dipole transitions from yellow to green excitons in cuprous oxide

Cited by in corpus (1)

• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities