Theory of the line shape of the 1S--2S transition for magnetically trapped antihydrogen

TL;DR

This paper develops a theoretical framework for understanding the line shape of the 1S--2S transition in magnetically trapped antihydrogen, aiming to simplify analysis and optimize experimental measurements.

Contribution

It introduces analytic formulas for the line shape in limiting cases and proposes a $$ method to select experimental parameters for precise frequency determination.

Findings

Analytic formulas for line shape in specific limits

A $$ method for optimizing experimental parameters

Illustrative calculations demonstrating assumptions' limits

Abstract

The physics that determines the line shape of the 1S--2S transition in magnetically trapped $\bar{\rm H}$ is explored. Besides obtaining an understanding of the line shape, one goal is to replace the dependence on large scale simulations of $\bar{\rm H}$ with a simpler integration over well defined functions. For limiting cases, analytic formulas are obtained. Example calculations are performed to illustrate the limits of simplifying assumptions. We also describe a $\chi^2$ method for choosing experimental parameters that can lead to the most accurate determination of the transition frequency.