Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3

TL;DR

This paper investigates quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3, finding that interference can affect measurements in muonic deuterium but is negligible in hydrogen and helium-3.

Contribution

It provides a theoretical analysis of quantum interference effects on Lamb shift measurements in muonic isotopes, with specific calculations relevant to experimental setups.

Findings

Quantum interference effects are negligible in muonic hydrogen and helium-3.

In muonic deuterium, interference can cause shifts up to a few percent of the linewidth.

Considering experimental geometry reduces the interference effect to below 0.2% of the linewidth.

Abstract

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy.