Laser spectroscopy of trapped short-lived Ra${}^{+}$ ions

As an important step toward an atomic parity violation experiment in one single trapped Ra${}^{+}$ ion, laser spectroscopy on short-lived ${}^{212,213,214}\mathrm{Ra}$${}^{+}$ ions was conducted. The isotope shift of the $6\hspace{0.5em}{}^2{D}_{3/2}$-$7\hspace{0.5em}{}^2{P}_{1/2}\hspace{0.5em}$and $6\hspace{0.5em}{}^2{D}_{3/2}$-$7\hspace{0.5em}{}^2{P}_{3/2}\hspace{0.5em}$transitions and the hyperfine structure constants of the $7\hspace{0.5em}{}^2{P}_{1/2}\hspace{0.5em}$and $6\hspace{0.5em}{}^2{D}_{3/2}\hspace{0.5em}$states in ${}^{213}\mathrm{Ra}$${}^{+}$ were measured, which provides a benchmark for the required atomic theory. A lower limit of $232(4)$ ms for $6\hspace{0.5em}{}^2{D}_{5/2}\hspace{0.5em}$state lifetime was determined.

Figure 1

${}^{213}\mathrm{Ra}$${}^{+}$ level scheme with wavelengths from Ref. [22]. Branching ratios and lifetimes are calculated in Ref. [18].

Figure 2

Schematic overview of the experimental setup behind the RFQ cooler.

Figure 3

HFS of the $6\hspace{0.5em}{}^2{D}_{3/2}$-$7\hspace{0.5em}{}^2{P}_{1/2}\hspace{0.5em}$transition in ${}^{213}\mathrm{Ra}$${}^{+}$. The solid line represents a fit of three Voigt profiles to the data. The Gaussian widths of the resonances are 181(20) MHz [full width at half maximum (FWHM)]. The Lorentzian widths (FWHM) are 245(20), 368(70), and 147(9) MHz (left to right). The different Lorentzian widths are due to saturation effects. The reduced ${\chi }^2=1.1$ at 62 degrees of freedom (DOF).

Figure 4

$6\hspace{0.5em}{}^2{D}_{3/2}$-$7\hspace{0.5em}{}^2{P}_{1/2}\hspace{0.5em}$resonances in ${}^{212}\mathrm{Ra}$${}^{+}$ and ${}^{214}\mathrm{Ra}$${}^{+}$. The solid line represents a fit of two Voigt profiles to the data. One parameter is used to fit the Gaussian widths of the two resonances, which yields a FWHM of 436(40) MHz. The Lorentzian widths (FWHM) are 201(50) MHz and 145(60) MHz (left to right). The reduced ${\chi }^2=0.92$ at $22$ DOF.

Figure 5

The $6\hspace{0.5em}{}^2{D}_{3/2}$-$7\hspace{0.5em}{}^2{P}_{3/2}\hspace{0.5em}$transitions. The solid lines represent fits of Voigt profiles to the data with reduced ${\chi }^2$’s of 0.81, 0.81, and 0.88 for ${}^{212}\mathrm{Ra}$${}^{+}$, ${}^{213}\mathrm{Ra}$${}^{+}$, and ${}^{214}\mathrm{Ra}$${}^{+}$, respectively, at 18, 26, and 17 DOF. The corresponding Gaussian and Lorentzian widths (FWHM) are 655(12) MHz and 243(10) MHz, respectively, for ${}^{212}\mathrm{Ra}$${}^{+}$, 363(30) and 144(23) MHz for the $F=2-F^{\prime }=1$ transition in ${}^{213}\mathrm{Ra}$${}^{+}$, and 451(270) MHz and 581(300) MHz for ${}^{214}\mathrm{Ra}$${}^{+}$. The different Gaussian widths are due to different neon buffer gas pressures. The different Lorentzian widths are caused by saturation effects which vary with gas pressure and laser power.

Figure 6

Lifetime of the ${}^{212}\mathrm{Ra}$${}^{+}$ $6\hspace{0.5em}{}^2{D}_{5/2}\hspace{0.5em}$state at a neon buffer gas pressure of $4\times {10}^{-5}$ mbar. The solid line represents a fit of an exponential function to the data. The fit yields a lifetime of 232(4) ms with a reduced ${\chi }^2=0.83$ at 87 DOF.