Fermi golden rule beyond the Zeno regime

TL;DR

This paper analyzes the spontaneous emission process of an excited atom beyond the Zeno regime, developing a perturbative approach to connect short-time and long-time dynamics, and compares different interaction Hamiltonians.

Contribution

It introduces a perturbative method to interpolate between Zeno, golden rule, and Wigner-Weisskopf regimes, enhancing understanding of atomic emission dynamics.

Findings

Survival probability is governed by coherent vacuum mode response in the Zeno regime.

Developed a perturbative approach bridging different temporal regimes.

Compared different interaction Hamiltonians and approximations.

Abstract

We reconsider the problem of the spontaneous emission of light by an excited atomic state. We scrutinize the survival probability of this excited state for very short times, in the so-called Zeno regime, for which we show that the dynamics is dictated by a coherent --in phase -- response of the on-shell and off-shell vacuum modes. We also develop a perturbative approach in order to interpolate between different temporal regimes: the Zeno, golden rule (linear) and Wigner-Weisskopf (exponential) regimes. We compare results obtained with the $\hat{\mathbf{E}}\cdot\hat{\mathbf{x}}$ and $\hat{\mathbf{A}}\cdot\hat{\mathbf{p}}$ interaction Hamiltonian,s, using successively the dipole approximation and the exact coupling.