# Rydberg states of helium in electric and magnetic fields of arbitrary relative orientation

## TL;DR

This paper investigates helium Rydberg states under various electric and magnetic field orientations, comparing experimental spectra with theoretical calculations to understand level interactions and mixing effects relevant for cold atom and molecule trapping.

## Contribution

It provides a detailed spectroscopic analysis of helium Rydberg states in arbitrary field orientations, including new insights into avoided crossings and $m_l$-mixing effects.

## Key findings

- Avoided crossings between different $m_l$ levels observed.
- Pronounced $m_l$-mixing effects at non-zero angles.
- Spectra well-matched with Hamiltonian eigenvalue calculations.

## Abstract

A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ($n$ = 30, $B \leq$ 120 mT and $F$ = 0 - 78 V/cm ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different $m_l$ values and pronounced $m_l$-mixing effects at all angles between the electric and magnetic field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.