Quantum interference in two-photon frequency-comb spectroscopy

Quantum interference arising from spontaneous emission, or cross-damping, is an important yet frequently overlooked systematic in precision spectroscopy experiments which aim to determine a transition frequency with an uncertainty smaller than the natural linewidth. Here, we calculate the effects of such interference in two-photon frequency-comb spectroscopy using a perturbative approach and by integration of the density matrix equations. We then apply these techniques to the two-photon spectroscopy of the hydrogen 1S-3S transition currently being performed in our group. Depending on the detection geometry, we find distortions of the line shapes which can lead to systematic errors of similar to 1 kHz if such interference effects are ignored in the data analysis. This result is independent of whether a cw laser or frequency comb is used for the excitation. Finally, we propose a time-dependent detection scheme which, when used in conjunction with frequency-comb excitation, can mitigate the line distortions arising from such interference.