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

TL;DR

This paper investigates how quantum interference between different resonant transitions can distort line shapes and cause shifts in measurements, exemplified by the hydrogen Lamb shift, due to decay pathways connecting distinct states.

Contribution

It introduces the concept of interference between resonant transitions with different initial and final states, revealing its impact on precision measurements.

Findings

Interference causes measurable shifts in resonance line shapes.

Decay pathways influence the accuracy of atomic transition measurements.

The effect is demonstrated in hydrogen 2S-2P transition measurements.

Abstract

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 2S$_{1/2}$-to-2P$_{1/2}$ Lamb-shift transition due to 3S-to-3P transitions if the 3S$_{1/2}$ state has some initial population.