Interference between two resonant transitions with distinct initial and final states connected by radiative decay

The resonant line shape from driving a transition between two states, $| {\rm a} \rangle$ and $| {\rm b} \rangle$, can be distorted due to a quantum-mechanical interference effect involving a resonance between two different states, $| {\rm c} \rangle$ and $| {\rm d} \rangle$, if $| {\rm c} \rangle$ has a decay path to $| {\rm a} \rangle$ and $| {\rm d} \rangle$ has a decay path to $| {\rm b} \rangle$. This interference can cause a shift of the measured resonance, despite the fact that the two resonances do not have a common initial or final state. As an example, we demonstrate that such a shift affects measurements of the atomic hydrogen $\textrm{2S}_{1/2}$-to-$\textrm{2P}_{1/2}$ Lamb-shift transition due to $\textrm{3S}$-to-$\textrm{3P}$ transitions if the $\rm 3S_{1/2} $ state has some initial population. Link: https://doi.org/10.1103/PhysRevA.96.062111