Angular correlations in two-photon spectroscopy of hydrogen

TL;DR

This paper analyzes angular correlations and quantum interference effects in two-photon hydrogen spectroscopy, deriving precise expressions for scattering cross sections and highlighting their impact on fundamental constant measurements.

Contribution

It provides rigorous quantum electrodynamics calculations of angular correlations and nonresonant corrections in two-photon hydrogen spectroscopy, including all atomic quantum numbers.

Findings

Nonresonant corrections can significantly affect measurements of the Rydberg constant.

Derived closed-form expressions for two-photon scattering cross sections with full quantum number dependence.

Demonstrated the importance of experimental geometry in two-photon spectroscopy accuracy.

Abstract

In the present paper, we consider nonresonant corrections to $ 2s-ns/nd $ transition frequencies in hydrogen for the experiments based on two-photon spectroscopy. A detailed study of angular correlations of quantum interference effects within the framework of rigorous quantum electrodynamics is given. Closed expressions for the resonant two-photon scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure are derived. These expressions are applied for the description of experiments based on two-photon spectroscopy with fixing of incident (outgoing) photon polarizations. We demonstrate that for certain experimental geometry nonresonant corrections could be significant for the determination of Rydberg constant and proton charge radius.