# Constraining the deformed dispersion relation with the hydrogen atom 1S-2S transition

## TL;DR

This study uses high-precision hydrogen atom spectroscopy to set experimental bounds on possible modifications to the dispersion relation at Planck-scale energies, demonstrating laboratory sensitivity to quantum gravity effects.

## Contribution

It provides the first constraints on deformed dispersion relations using the hydrogen 1S-2S transition, improving bounds from previous cold-atom experiments.

## Key findings

- Leading correction constrained at Planck-scale sensitivity.
- Next-to-leading term bound is two orders of magnitude away from Planck scale.
- First laboratory bounds on deformed dispersion relations using hydrogen spectroscopy.

## Abstract

In this paper, we use the latest results of the ultra-high accuracy 1S-2S transition experiments in hydrogen atom to constrain the forms of the deformed dispersion relation in the nonrelativistic limit. For the leading correction of the nonrelativistic limit, the experiment sets a limit at an order of magnitude for the desired Planck-scale level, thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments. And for the next-to-leading term, bound has two orders of magnitude away from the Planck scale, but it still amounts to the best limit, in contrast to previously obtained bound in the nonrelativistic limit from the cold-atom-recoil experiments.