Quantum jumps in hydrogen-like systems

In this paper it is shown that the Lyman-$\alpha$ transition of a single hydrogen-like system driven by a laser exhibits macroscopic dark periods, provided there exists an additional constant electric field. We describe the photon-counting process under the condition that the polarization of the laser coincides with the direction of the constant electric field. The theoretical results are given for the example of $^4{He}^+$. We show that the emission behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford, Phys. Rev. 72, 241 (1947)) between the $2s_{1/2}$ and $2p_{1/2}$ energy levels. A possibly realizable measurement of the mean duration of the dark periods should give quantitative information about the above energy difference by using the proposed photon-counting process.