# Simulations of Majorana spin flips in an antihydrogen trap

## TL;DR

This paper investigates the occurrence and effects of magnetic field zeros on Majorana spin flips in antihydrogen traps, providing insights for experiments at very low magnetic fields.

## Contribution

It analyzes the properties of magnetic field zeros in antihydrogen traps and models their impact on spin flip probabilities, especially near quadratic zeros.

## Key findings

- Magnetic field zeros occur as two groups of 5 points in typical geometries.
- Zeros can be treated as independent sources of spin flip probability.
- Results suggest minimal impact of higher order zeros on spin flips in traps.

## Abstract

The properties of antihydrogen ($\bar{\rm H}$) have, thus far, been probed at magnetic fields of $\sim 1$ T. It may be fruitful to perform some of these measurements at magnetic fields approaching 0 T. In this case, there could occur zeros in the magnitude of the $B$-field. The number and properties of the magnetic field zeros are investigated. For typical magnetic field geometries in $\bar{\rm H}$ traps, the zeros will occur as two groups of 5 closely spaced points instead of as a single point. Except in special cases, results from calculations show that these 10 zeros can be treated as independent sources of spin flip probability. Although the behavior of Majorana spin flip near higher order zeros should not be important in the $\bar{\rm H}$ traps, the probability for spin flip is calculated for the case of a quadratic zero. Finally, results are presented for a simple model of how magnetic field zeros would affect the trapped population of $\bar{\rm H}$.