# Gravitational Searches for Lorentz Violation with Ultracold Neutrons

## TL;DR

This paper explores how Lorentz violation could affect gravitational quantum states of ultracold neutrons and uses experimental data to set bounds on Lorentz-violating parameters within the Standard-Model Extension framework.

## Contribution

It provides a theoretical analysis of Lorentz violation effects on UCN gravitational states and compares predictions with experimental results to constrain Lorentz-violating coefficients.

## Key findings

- Derived effective Hamiltonian for UCNs in a Lorentz-violating gravity background
- Calculated energy level shifts due to Lorentz violation
- Established upper bounds on Lorentz-violating coefficients from GRANIT experiment data

## Abstract

We investigate the consequences of Lorentz violation (as expressed within the gravity sector of the Standard-Model Extension) for gravitational quantum states of ultracold neutrons (UCNs). Since our main aim is to compare our theoretical results with the recent high-sensitivity GRANIT experiment, we frame this work according to the laboratory conditions under which it was carried out. This offers the possibility of testing Lorentz invariance by experiments using UCNs. Thus we consider the nonrelativistic Hamiltonian describing the quantum mechanics of an unpolarized neutron's beam in presence of a weak-gravity field, and the latter is described by a post-Newtonian expansion of the metric up to order $O (2)$ and linear in the Lorentz-violating coefficients $\bar{s} ^{\mu \nu}$. Using a semi-classical wave packet, which is appropriate to describe an intense beam of UCNs, we derive the effective Hamiltonian describing the neutron's motion along the axis of free fall and then we compute the Lorentz-violating shifts on the energy levels. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for a particular combination of the Lorentz-violating coefficients.