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Physical Review A

Lifetime, collisional-quenching, andj-mixing measurements of the metastable 3Dlevels of Ca+

Martina Knoop, M. Vedel, F. Vedel

Published Nov 1, 1995• 50 citations
Publisher

Abstract

The metastable ${3}^{2}$${\mathit{D}}_{3/2,5/2}$ doublet of ${\mathrm{Ca}}^{+}$ 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}(${\mathit{D}}_{3/2}$)=1111\ifmmode\pm\else\textpm\fi{}46 ms and \ensuremath{\tau}(${\mathit{D}}_{5/2}$)=994\ifmmode\pm\else\textpm\fi{}38 ms, which agree very well with previous experiments. The estimation of the quenching rates of ${\mathrm{Ca}}^{+}$-He [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}$=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], ${\mathrm{Ca}}^{+}$-Ne [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{}\mathrm{Ne}}$=(0.9\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], and ${\mathrm{Ca}}^{+}$-${\mathrm{N}}_{2}$ [${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{N}}_{2}}$=(1.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] 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{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{35}$(${\mathrm{N}}_{2}$)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$] 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{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{53}$(${\mathrm{N}}_{2}$)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.

DOI
10.1103/physreva.52.3763

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In light of the diverse range of reported values for the lifetimes of metastable states of ${}^{40}{\mathrm{Ca}}^{+}$, we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its $3d\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}$ state $({\ensuremath{\tau}}_{3d5/2})$. A high-efficiency quantum state detection method by monitoring the quantum jumps of a laser-cooled single ${\mathrm{Ca}}^{+}$ 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)].

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The metastable {3}^{2}$${\mathit{D}}_{3/2,5/2} doublet of Ca+{\mathrm{Ca}}^{+}Ca+ ions stored in a Paul trap was investigated in the presence of different neutral gases, in the pressure range 10\ensuremath−9{10}^{\mathrm{\ensuremath{-}}9}10\ensuremath−9--10\ensuremath−6{10}^{\mathrm{\ensuremath{-}}6}10\ensuremath−6 mbar. The natural lifetimes were determined to be \ensuremath{\tau}(D3/2{\mathit{D}}_{3/2}D3/2​)=1111\ifmmode\pm\else\textpm\fi{}46 ms and \ensuremath{\tau}(D5/2{\mathit{D}}_{5/2}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+{\mathrm{Ca}}^{+}Ca+-He [\ensuremathΓHe{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}\ensuremathΓHe​=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}10\ensuremath−12{10}^{\mathrm{\ensuremath{-}}12}10\ensuremath−12 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1], Ca+{\mathrm{Ca}}^{+}Ca+-Ne [\ensuremathΓNe{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{}\mathrm{Ne}}\ensuremathΓNe​=(0.9\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}10\ensuremath−12{10}^{\mathrm{\ensuremath{-}}12}10\ensuremath−12 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1], and Ca+{\mathrm{Ca}}^{+}Ca+-N2{\mathrm{N}}_{2}N2​ [\ensuremathΓN2{\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{N}}_{2}}\ensuremathΓN2​​=(1.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}10\ensuremath−10{10}^{\mathrm{\ensuremath{-}}10}10\ensuremath−10 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\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 [\ensuremathγ35{\ensuremath{\gamma}}_{35}\ensuremathγ35​(He)=(2.24\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}10\ensuremath−10{10}^{\mathrm{\ensuremath{-}}10}10\ensuremath−10 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1 and \ensuremathγ35{\ensuremath{\gamma}}_{35}\ensuremathγ35​(N2{\mathrm{N}}_{2}N2​)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}10\ensuremath−9{10}^{\mathrm{\ensuremath{-}}9}10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1] and for the j=5/2\ensuremath{\rightarrow}j=3/2 case [\ensuremathγ53{\ensuremath{\gamma}}_{53}\ensuremathγ53​(He)=(1.2\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}10\ensuremath−10{10}^{\mathrm{\ensuremath{-}}10}10\ensuremath−10 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1 and \ensuremathγ53{\ensuremath{\gamma}}_{53}\ensuremathγ53​(N2{\mathrm{N}}_{2}N2​)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}10\ensuremath−9{10}^{\mathrm{\ensuremath{-}}9}10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1]. The measurements were carried out populating the metastable levels by direct laser excitation of the forbidden S-D transitions.
Collisional relaxation and fine-structure mixing rate constants have been measured for the metastable DDD doublet (3D3/2,{(3D}_{3/2},(3D3/2​, 3D5/2){3D}_{5/2})3D5/2​) of Ca+{\mathrm{Ca}}^{+}Ca+ ions in the presence of different neutral gases completing a previous work. Experimental results are given for He, Ne, Ar, H2,{\mathrm{H}}_{2},H2​, N2,{\mathrm{N}}_{2},N2​, and CH4.{\mathrm{CH}}_{4}.CH4​. These data have been obtained with a cloud of approximately 105{10}^{5}105 Ca+{\mathrm{Ca}}^{+}Ca+ ions stored in a Paul trap at kinetic energies of around 1 eV. The investigated levels were populated by direct excitation of the corresponding $4S\ensuremath{-}3D$ transitions. The involved time constants were determined from the temporal evolution of the fluorescence of one of the resonance transitions, following the optical pumping of the PPP level from the DDD component. Comparison of our data with other similar experimental and theoretical work is finally presented.
We report measurements of the lifetimes of the 3d2D5∕23d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}3d2D5∕2​ and 3d2D3∕23d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}3d2D3∕2​ metastable states of a single laser-cooled 40Ca+^{40}\mathrm{Ca}^{+}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{D}_{5∕2}D5∕2​ state or incoherent shelving in the D3∕2{D}_{3∕2}D3∕2​ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the D5∕2{D}_{5∕2}D5∕2​ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the D3∕2{D}_{3∕2}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{D}_{3∕2}D3∕2​ state: 1196(11) ms; D5∕2{D}_{5∕2}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+{\mathrm{Ba}}^{+}Ba+ which has similar atomic structure.
Ca + ions confined as a cloud in a Paul trap were excited and cooled by radiation from two lasers, tuned to the 4s 2 S 1/2 − 4p 2 P 1/2 and 4p 2 P 1/2 − 3d 2 D 3/2 transitions. The strong fluorescence of these lines disappears when we excite the ions simultaneously by a third laser on the 3d 2 D 3/2 − 4p 2 P 3/2 line because of population trapping in the metastable 3d 2 D 5/2 state, into which the 4p 2 P 3/2 level decays. From the time dependence of the fluorescence after blocking the third laser we determined the lifetime of the 3d 2 D 5/2 level. Our result of τ = 1064(17) ms improves earlier results and agrees with the value recently computed by Liaw using the Brueckner approximation.
We report a measurement of the lifetime of the 3d2D5/23d{}^{2}{D}_{5/2}3d2D5/2​ metastable level in 40Ca+,{}^{40}{\mathrm{Ca}}^{+},40Ca+, using quantum jumps of a single cold calcium ion in a linear Paul trap. The 4s2S1/2−−3d2D5/24s{}^{2}{S}_{1/2}--3d{}^{2}{D}_{5/2}4s2S1/2​−−3d2D5/2​ transition is significant for single-ion optical frequency standards, astrophysical references, and tests of atomic structure calculations. We obtain $\ensuremath{\tau}=1.168\ifmmode\pm\else\textpm\fi{}0.007$ s from observation of nearly 640006400064000 quantum jumps during $\ensuremath{\sim}32$ h. Our result is more precise and significantly larger than previous measurements. Experiments carried out to quantify systematic effects included a study of a previously unremarked source of systematic error, namely, excitation by the broad background of radiation emitted by a semiconductor diode laser. Combining our result with atomic structure calculations yields $1.20\ifmmode\pm\else\textpm\fi{}0.01$ s for the lifetime of 3d2D3/2.3d{}^{2}{D}_{3/2}.3d2D3/2​. We also use quantum jump observations to demonstrate photon antibunching, and to estimate background pressure and heating rates in the ion trap.
The extremely long lifetimes of the metastable DDD states of the Ba+{\mathrm{Ba}}^{+}Ba+ ion make it difficult to measure them accurately due to their high sensitivity to collisional effects. Thus a discrepancy exists between theories and experiments for the Ba+{\mathrm{Ba}}^{+}Ba+ D3/2{D}_{3/2}D3/2​ state. We have measured the D3/2{D}_{3/2}D3/2​ lifetime under a nearly ideal condition, i.e., single trapped Ba+{\mathrm{Ba}}^{+}Ba+ ions in ultrahigh vacuum. The obtained value of $79.8\ifmmode\pm\else\textpm\fi{}4.6\mathrm{s}$ resolves the existing discrepancy. The collisional quenching is found insignificant in our experiment, but there are indications of a non-negligible fine-structure mixing effect.
In light of the diverse range of reported values for the lifetimes of metastable states of 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+, we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its 3d2D5/23d\phantom{\rule{0.16em}{0ex}}{}^{2}{D}_{5/2}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+{\mathrm{Ca}}^{+}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)].