Fingerprints of exceptional points in the survival probability of resonances in atomic spectra

2011/04/30 by Holger Cartarius, Nimrod Moiseyev · 1 citation
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #nlin.CD #physics.atom-ph

paper · pdf · doi:10.1103/physreva.84.013419

published as Phys. Rev. A 84, 013419 (2011) · 6 pages, 3 figures, additional references and comments in the text

arxiv created 2011/06/28 · openalex publication_date 2011/07/25 · arxiv updated 2011/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability S(t)=|\ensuremath⟨\ensuremathψ(0)|\ensuremathψ(t)\ensuremath⟩|² decays exactly as |1\ensuremath-at|²e^\ensuremath-\ensuremathΓ_EPt/\ensuremathℏ, where \ensuremathΓ_EP is associated with the decay rate at the exceptional point and a is a complex constant depending solely on the initial wave packet that populates exclusively the two almost degenerate states of the non-Hermitian Hamiltonian. This may open the possibility for a first experimental detection of exceptional points in a quantum system.

Citations

• Asymmetric scattering and nonorthogonal mode patterns in optical microspirals
• Wannier-Stark resonances in optical and semiconductor superlattices
• Exceptional points in the spectra of atoms in external fields
• A non-Hermitian PT symmetric Bose–Hubbard model: eigenvalue rings from unfolding higher-order exceptional points

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