Collective magnetic splitting in single-photon superradiance

TL;DR

This paper develops a formalism to analyze how collective effects in multi-level atomic or nuclear systems under magnetic fields cause measurable deviations in energy level splitting, especially in nuclear hyperfine structures.

Contribution

It introduces a new formalism for single-photon superradiance in multi-level systems and quantifies conditions for observable collective Lamb shifts in magnetic splitting.

Findings

Collective Lamb shift can cause significant deviations from single-atom Zeeman splitting.

The formalism applies to nuclear hyperfine splitting in M"ossbauer nuclei.

Observable effects are predicted in thin-film x-ray cavity experiments.

Abstract

In an ensemble of identical atoms, cooperative effects like sub- or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multi-level systems are more difficult to handle. In this work we show that in a system of atoms or nuclei under the action of an external magnetic field, the collective contribution to the level shifts can amount to seizable deviations from the single-atom Zeeman or magnetic hyperfine splitting picture. We develop a formalism to describe single-photon superradiance in multi-level systems in the small sample limit and quantify the parameter regime for which the collective Lamb shift leads to measurable deviations in the magnetic-field-induced splitting. In particular, we show that this effect should be observable in the nuclear magnetic hyperfine splitting in M\"ossbauer nuclei embedded in thin-film x-ray cavities.