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

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)=|<psi(0)|psi(t)>|^2 decays exactly as |1-a*t|^2 e^(-Gamma_EP*t/hbar) where Gamma_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.

arXiv comment6 pages, 3 figures, additional references and comments in the text

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Cited by in corpus (24)

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• State Flip at Exceptional Points in Atomic Spectra
• Optical lattices with exceptional points in the continuum
• Wave emission and absorption at spectral singularities
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Quantum interference and exceptional points
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
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• Quantum decay in a topological continuum
• Harmonic inversion analysis of exceptional points in resonance spectra
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Detecting exceptional points through dynamics in non-Hermitian systems
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Emergent Liouvillian exceptional points from exact principles
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates
• Quantum jumps in open cavity optomechanics and Liouvillian versus Hamiltonian exceptional points
• Characteristic influence of exceptional points in quantum dynamics