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.