Precision measurement of the ionization energy of a single trapped $^{40}$Ca$^+$ ion by Rydberg series excitation

TL;DR

This paper precisely measures the ionization energy of a single trapped $^{40}$Ca$^+$ ion using Rydberg series spectroscopy, achieving a 60-fold improvement in accuracy over previous values and confirming quantum defect parameters.

Contribution

It provides the most accurate ionization energy measurement for $^{40}$Ca$^+$ and confirms quantum defect values, aiding quantum information processing with Rydberg states.

Findings

Ionization energy measured as 2 870 575.582(15) GHz, 60 times more accurate.

Quantum defect values for $nS_{1/2}$ and $nD_{5/2}$ states confirmed.

Measurement contradicts previous accepted value by 7.5 standard deviations.

Abstract

A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ and for $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ ion. From a nonlinear regression to resonance frequencies, we determined the ionization energy of 2 870 575.582(15) GHz, measured 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of $\delta_{S_{1/2}}=1.802995(5)$ and $\delta_{D_{5/2}}=0.626888(9)$ for $nS_{1/2}$ and $nD_{5/2}$ states respectively, which allow for unambiguous addressing of Rydberg levels of Ca$^+$ ions.