In light of the diverse range of reported values for the lifetimes of metastable states of
40Ca+, we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its
3d2D5/2 state $({\ensuremath{\tau}}_{3d5/2})$. A high-efficiency quantum state detection method by monitoring the quantum jumps of a laser-cooled single
Ca+ ion in a miniature ring Paul trap was employed in the measurement. Also, sophisticated calculations were performed considering higher order nonlinear terms in the relativistic coupled-cluster (RCC) method with all possible single and double excitations, but accounting only for the important triple excitations from both the core and the valence orbitals. Systematic factors affecting measurement, such as collision with background gases, heating effects, the power of the 866-nm laser, and state detection errors were carefully analyzed. Our observational and theoretical values for ${\ensuremath{\tau}}_{3d5/2}$ are 1174(10) ms and 1172(3) ms, respectively, which agree well with the experimental results reported by P. A. Barton et al. [Phys. Rev. A 62, 032503 (2000)] and A. Kreuter et al. [Phys. Rev. A 71, 032504 (2005)]. The present theoretical analysis demonstrates that the contributions from the core triples and Breit interaction are notable, as they improve the theoretical results obtained in the previous RCC calculations [B. K. Sahoo, Phys. Rev. A 74, 062504 (2006)].
We report measurements of the lifetimes of the
3d2D5∕2 and
3d2D3∕2 metastable states of a single laser-cooled
40Ca+ ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the
D5∕2 state or incoherent shelving in the
D3∕2 state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the
D5∕2 state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the
D3∕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 [
D3∕2 state: 1196(11) ms;
D5∕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
Ba+ which has similar atomic structure.
We present a high-precision measurement of the
3d2D3/2--state lifetime in a single trapped
40Ca+. The measurement was performed using a high-efficiency quantum-state detection technique to monitor quantum jumps and a high-precision and highly synchronous measurement sequence for laser control. A feature in our measurement is the pumping rate of the 729-nm laser that was corrected in a real-time way. The
3d2D3/2--state lifetime was obtained through the measurement of the spontaneous decay rate after incoherent shelving of the ion to the
3d2D3/2 state with a wait time. Systematic errors, such as collisions with background gases, heating effects, impurity components, the shelving and pumping rates, and state detection, were carefully analyzed and estimated. We determined an improved value of the
3d2D3/2--state lifetime to be ${\ensuremath{\tau}}_{3/2}=1.195(8)$ s. Furthermore, the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}\ensuremath{\rightarrow}4s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}$ quadrupole transition matrix element was measured to be
Ski=7.936(26)ea02, and the ratio between the lifetimes of
3d2D3/2 and
3d2D5/2 was determined to be 1.018(11). Our method can be universally applied to lifetime measurements of other single ions and atoms with a similar structure.
The metastable
32D3/2,5/2 doublet of
Ca+ ions stored in a Paul trap was investigated in the presence of different neutral gases, in the pressure range ${10}^{\mathrm{\ensuremath{-}}9}$--${10}^{\mathrm{\ensuremath{-}}6}$ mbar. The natural lifetimes were determined to be \ensuremath{\tau}(
D3/2)=1111\ifmmode\pm\else\textpm\fi{}46 ms and \ensuremath{\tau}(
D5/2)=994\ifmmode\pm\else\textpm\fi{}38 ms, which agree very well with previous experiments. The estimation of the quenching rates of
Ca+-He [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}$=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$],
Ca+-Ne [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{}\mathrm{Ne}}$=(0.9\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], and
Ca+-
N2 [${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{N}}_{2}}$=(1.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] was carried out for collisions in the energy range 0.3--1.3 eV. In addition, rate constants for the mixing of the fine-structure states were measured in the presence of helium and nitrogen for the j=3/2\ensuremath{\rightarrow}j=5/2 case [${\ensuremath{\gamma}}_{35}$(He)=(2.24\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{35}$(
N2)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] and for the j=5/2\ensuremath{\rightarrow}j=3/2 case [${\ensuremath{\gamma}}_{53}$(He)=(1.2\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{53}$(
N2)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.
Abstract We present for the first time a direct measurement of the lifetime ratio between the 3 d 2 D 3 / 2 and 3 d 2 D 5 / 2 metastable states in a single trapped 40 Ca + . A high-efficiency quantum state detection technique is adopted to monitor the quantum jumps, and a high precision and synchronized measurement sequence is used for laser control to study the rule of spontaneous decay. Our method shows that the lifetime ratio is a constant and is irrelevant to the dwell time; it is only determined by the spontaneous decay probabilities of the two metastable states at one random decay time, independent of the lifetimes of the two metastable states. Systematic errors such as collisions with background gases, heating effects, impurity components, the shelving and pumping rates and the photon counts are analyzed, and the lifetime ratio between the 3 d 2 D 3 / 2 and 3 d 2 D 5 / 2 states is directly measured to be 1.0257(43) with an uncertainty of 0.42%. Our result is in good agreement with the most precise many-body atomic structure calculations. Our method can be used to obtain the lifetime of a state which is usually difficult to measure and can be used to determine the magnetic dipole transition matrix elements in heavy ions such as Ba + and Ra + , and can also be universally applied to lifetime ratio measurements of other single atoms and ions with a similar structure.
We present a measurement of the lifetime of the metastable
3d2D5∕2 state in the
40Ca+ ion, using the so-called shelving technique on a string of five Doppler laser-cooled ions in a linear Paul trap. A detailed account of the data analysis is given, and systematic effects due to unwanted excitation processes and collisions with background gas atoms are discussed and estimated. From a total of 6805 shelving events, we obtain a lifetime $\ensuremath{\tau}=1149\ifmmode\pm\else\textpm\fi{}14(\text{stat}.)\ifmmode\pm\else\textpm\fi{}4(\text{sys}.)\text{ms}$, a result which is in agreement with the most recent measurements.