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

TL;DR

This paper investigates the unique decay signature of survival probability at exceptional points in atomic spectra, suggesting a potential method for experimental detection of these points in quantum systems.

Contribution

It demonstrates the exact decay form of survival probability at exceptional points in a hydrogen atom under strong fields, linking it to observable decay rates and initial conditions.

Findings

Survival probability decays as |1 - a*t|^2 e^(-Gamma_EP*t/hbar) at exceptional points

Decay rate Gamma_EP is associated with the exceptional point

Initial wave packet influences the decay through a complex constant a

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.