Modulated Exponential Decay in a Two-Level Quantum System

Abstract

We carry out a Weisskopf-Wigner-type calculation for a system of two quantum levels which are simultaneously coupled by a quantized radiation interaction $H$ and a classical external perturbation $V$. The results for the level populations properly reduce to the quantum oscillation solution when $H\to 0$ and to the exponential-decay solution when $V\to 0$. When neither $H$ nor $V$ is zero, the upper level undergoes a modulated exponential decay. We derive an expression for the perturbed decay rate and discover a new type of modulation factor. The result suggests possibly important modifications to the standard, phenomenological solution of the three-level $H+V$ problem, which is of practical interest.