# Determination of quantum defect for the Rydberg P series of Ca II

## TL;DR

This paper experimentally investigates the Rydberg 23 P$_{1/2}$ state of laser-cooled Ca$^+$ ions, precisely characterizes electric fields, and determines the quantum defect and ionization energy, confirming existing values.

## Contribution

It provides a new precise measurement of the quantum defect and ionization energy for Ca II Rydberg P states using advanced spectroscopic techniques.

## Key findings

- Ionization energy of 95,751.916(32) cm$^{-1}$ was determined.
- Quantum defect for n P$_{1/2}$ states was measured.
- Electric field effects on Rydberg transitions were minimized.

## Abstract

We present an experimental investigation of the Rydberg 23 P$_{1/2}$ state of laser-cooled $^{40}$Ca$^+$ ions in a radiofrequency ion trap. Using micromotion sideband spectroscopy on a narrow quadrupole transition, the oscillating electric field at the ion position was precisely characterised, and the modulation of the Rydberg transition due to this field was minimised. From a correlated fit to this P line and previously measured P and F level energies of Ca II, we have determined the ionization energy of 95 751.916(32) $\rm {cm}^{-1}$, in agreement with the accepted value, and the quantum defect for the $n$ P$_{1/2}$ states.