Experimental and theoretical study of the $3d{}^{2}D$–level lifetimes of ${}^{40}\mathrm{Ca}^{+}$

We report measurements of the lifetimes of the $3d{}^{2}D_{5∕2}$ and $3d{}^{2}D_{3∕2}$ metastable states of a single laser-cooled ${}^{40}\mathrm{Ca}^{+}$ ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the $D_{5∕2}$ state or incoherent shelving in the $D_{3∕2}$ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the $D_{5∕2}$ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the $D_{3∕2}$ state is measured with a single ion and yields 1176(11) ms which improves the statistical uncertainty of previous results by a factor of four. We compare these experimental lifetimes to high-precision ab initio all order calculations [$D_{3∕2}$ state: 1196(11) ms; $D_{5∕2}$ state: 1165(11) ms] and find a very good agreement. These calculations represent an excellent test of high-precision atomic theory and will serve as a benchmark for the study of parity nonconservation in ${\mathrm{Ba}}^{+}$ which has similar atomic structure.

Figure 1

${\mathrm{Ca}}^{+}$-level scheme with relevant transitions.

Figure 2

Theoretical and experimental results for the $D_{5∕2}$-level lifetime.

Figure 3

Theoretical and experimental results for the $D_{3∕2}$-level lifetime.

Figure 4

Simplified pulse scheme for the $D_{5∕2}$ lifetime measurement: the preparation consists of Doppler cooling, repumping, and optical pumping (2 ms), followed by a $\pi$ pulse (few $\mu \mathrm{s}$) and detection periods (3.5 ms). The waiting time is varied between 25 ms and 5 s.

Figure 5

$D_{5∕2}$-level excitation probability after delay times from 25 ms to 5 s plotted on a logarithmic scale. The solid line is a least squares fit to the data yielding ${\tau }_{(5∕2)}=1168\left(9\right)\mathrm{ms}$. The residuals (difference of data points and fit curve) of the fit are shown in the lower diagram.

Figure 6

Simplified pulse scheme for the $D_{3∕2}$ lifetime measurement. It consists of a measurement of the $\pi$-pulse transfer efficiency on the $S_{1∕2}\text{−}{D}_{5∕2}$ transition (prep, $\pi$, and det1); $D_{3∕2}$-state preparation (prep, s); waiting period $\mathrm{\Delta }t$ and state detection ($\pi$ and det2). For details of the pulse sequence, see text. The waiting time is varied between 25 ms and 5 s.

Figure 7

$D_{3∕2}$-level excitation probability for delay times from 25 ms to 2 s plotted on a logarithmic scale. The solid line is a least squares fit to the data yielding ${\tau }_{(3∕2)}=1176\left(11\right)\mathrm{ms}$. The residuals (difference of data points and fit curve) of the fit are shown in the lower diagram.

Figure 8

Average transfer efficiency of the $\pi$ pulses on the $S_{1∕2}$ to $D_{5∕2}$ transition after various delay times between Doppler cooling and $\pi$ pulses.