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

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 $n{S}_{1/2}$ states with $38\le n\le 65$ and for $n{D}_{5/2}$ states with $37\le n\le 50$ 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 $n{S}_{1/2}$ and $n{D}_{5/2}$ states respectively, which allow for unambiguous addressing of Rydberg levels of Ca${}^{+}$ ions.

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