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.

6 pages, 3 figures, additional references and comments in the text

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• Signatures of Liouvillian exceptional points in a quantum thermal machine
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• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• 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
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates
• Emergent Liouvillian exceptional points from exact principles
• Quantum jumps in open cavity optomechanics and Liouvillian versus Hamiltonian exceptional points
• Characteristic influence of exceptional points in quantum dynamics