Precision Isotope Shift Measurements in Calcium Ions Using Quantum Logic Detection Schemes

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the ${}^2{D}_{3/2}\to {}^2{P}_{1/2}$ transition in calcium, resulting in a transition frequency of $f=346000234867(96)\mathrm{kHz}$. Furthermore, we determine the isotope shift of this transition and the ${}^2{S}_{1/2}\to {}^2{P}_{1/2}$ transition for ${}^{42}{\mathrm{Ca}}^{+}$, ${}^{44}{\mathrm{Ca}}^{+}$, and ${}^{48}{\mathrm{Ca}}^{+}$ ions relative to ${}^{40}{\mathrm{Ca}}^{+}$ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.

Figure 1

Experimental sequence for the spectroscopy on (a) the ${}^2{S}_{1/2}\to {}^2{P}_{1/2}$ transition and (b) the ${}^2{D}_{3/2}\to {}^2{P}_{1/2}$ transition. A detailed description is given in the text. (c) Simplified level scheme of ${\mathrm{Ca}}^{+}$ ions.

Figure 2

Overlapped Allan deviation ${\sigma }_y(\tau )$ of the frequency measurement of the ${}^2{D}_{3/2}\to {}^2{P}_{1/2}$ transition of ${}^{40}{\mathrm{Ca}}^{+}$. The inset shows a resonance scan of the transition, where the red line corresponds to density matrix simulations adjusted in amplitude and offset to account for experimental imperfections.

Figure 3

Two-dimensional King plot showing the modified isotope shift of the 866 nm and 397 nm lines. Red squares, previous experimental data from [10] and [11]; blue circles, this Letter. The insets show the relevant ranges enlarged by a factor of approximately 30 to illustrate the quality of the fit.