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Physical Review A

Collisional quenching and j -mixing rate constants for the 3D levels of Ca+

Martina Knoop, M. Vedel, F. Vedel

Published Jul 1, 1998• 20 citations
Publisher

Abstract

Collisional relaxation and fine-structure mixing rate constants have been measured for the metastable $D$ doublet ${(3D}_{3/2},$ ${3D}_{5/2})$ of ${\mathrm{Ca}}^{+}$ ions in the presence of different neutral gases completing a previous work. Experimental results are given for He, Ne, Ar, ${\mathrm{H}}_{2},$ ${\mathrm{N}}_{2},$ and ${\mathrm{CH}}_{4}.$ These data have been obtained with a cloud of approximately ${10}^{5}$ ${\mathrm{Ca}}^{+}$ 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 $P$ level from the $D$ component. Comparison of our data with other similar experimental and theoretical work is finally presented.

DOI
10.1103/physreva.58.264

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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.

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Alan A. Madej, J. D. Sankey

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Kinetic study of Ca(4 3 PJ) by time-resolved emission, 4 3 P 1 → 4 1 S 0 +hν(λ= 657.3 nm), following dye-laser excitation. Spontaneous emission, diffusion and collisional quenching

David Husain, José Schifino

We present a kinetic study of the low-lying electronically excited state of atomic calcium, Ca[4s4p(3PJ)], 1.885 eV above the 4s2(1S0) ground state. Ca(4 3P1) was generated by dye-laser pulsed excitation at λ= 657.3 nm of calcium vapour [Ca(4 3P1)â†� Ca(4 1S0)] at elevated temperatures (1000 K), in equilibrium with solid calcium, in a slow-flow system, kinetically equivalent to a static system. Following rapid Boltzmann equilibration within Ca(4 3PJ) through collisions, the forbidden time-resolved atomic resonance fluorescence at the same wavelength was monitored using boxcar integration. The decay of Ca(4 3PJ) in the presence of all the noble gases, He, Ne, Ar, Kr and Xe, was studied, yielding measurements of relative diffusion coefficients. Extrapolation of the diffusional component of the decay in each noble gas to infinite pressure yields an independent value of the mean radiative lifetime for Ca(4 3P1)→ Ca(4 1S0)+hν(λ= 657.3 nm), the average of which from the measurements in all the noble gases yields τe= 0.34 ± 0.02 ms (error 2σ). This result is compared with values reported from previous measurements, particularly atomic beams and time-resolved measurements. The kinetic analysis also gives rise to data for the collisional quenching of Ca(4 3PJ), which is found to be insignificant for most of the noble gases [kHe,Ne,Ar,Kr⩽ 4 × 10–15 cm3 molecule–1 s–1(1000 K)], in contrast to measurements from earlier work using phase-shift techniques. Xenon, however, exhibited measurable rates of collisional quenching of Ca(4 3PJ) characterised by kXe= 2.4 ± 0.3 × 10–14 cm3 molecule–1 s–1(1000 K). The time-resolved emission technique is further applied to the study of the removal of Ca(4 3PJ) by added gases, for which we report (errors 1σ)kN2=(8.9 ± 0.9)× 10–13 cm3 molecule–1 s–1(1000 K), kH2=(6.0 ± 0.6)× 10–14 cm3 molecule–1 s–1(1000 K), kD2=(2.7 ± 0.3)× 10–14 cm3 molecule–1 s–1(1000 K).

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arXiv:physics/0409038•Physical Review A•Mar 11, 2005•105 citations
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−3D4S\ensuremath{-}3D4S\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.
The metastable 32{3}^{2}32D3/2,5/2{\mathit{D}}_{3/2,5/2}D3/2,5/2​ 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 ${10}^{\mathrm{\ensuremath{-}}9}$--${10}^{\mathrm{\ensuremath{-}}6}$ 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 [${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{He}}$=(1.05\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], Ca+{\mathrm{Ca}}^{+}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{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], and Ca+{\mathrm{Ca}}^{+}Ca+-N2{\mathrm{N}}_{2}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{cm}}^{3}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{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{35}$(N2{\mathrm{N}}_{2}N2​)=(2.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ cm3{\mathrm{cm}}^{3}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{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${\ensuremath{\gamma}}_{53}$(N2{\mathrm{N}}_{2}N2​)=(1.26\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}9}$ cm3{\mathrm{cm}}^{3}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.
In order to exploit the capability of a high-Q transition for a frequency standard in the optical domain (729 nm), a stored Ca+ ion cloud in a medium-size ion trap is investigated. Long confinement times are obtained in the presence of helium as a buffer gas in the range 10-6-10-8 mbar and at a pseudopotential well depth of 62 eV. First observations of the electric quadrupole line were achieved by direct excitation of one of the first metastable doublet levels (τ≈1 s). Utilisation of a grating-stabilised diode laser in order to probe both levels when only one level is initially populated allows us to observe almost equal fluorescence intensities of both forbidden lines that show the presence of a strong fine structure mixing which exists in addition to quenching.
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.
A single Ba+{\mathrm{Ba}}^{+}Ba+ atom was confined in a radio-frequency ion trap and cooled by near-resonant laser light. Quantum jumps into and out of the metastable 5d 2D5/2^{2}D_{5/2}2D5/2​ level were observed that followed the expected exponential distribution in dark periods to good agreement. Measurement of quantum-jump distributions together with careful measurements of the absolute partial pressures of all residual gas species enabled accurate measurements of the quenched 5d 2D5/2^{2}D_{5/2}2D5/2​ lifetime as a function of quenching gas pressure. Measurements of quenching were observed at pressures where the mean collision rate was on the order of 1 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The results yielded quenching rate constants for the metastable level for a series of gases that typically make up the residual gas environment of ultra-high-vacuum systems (H2{\mathrm{H}}_{2}H2​, He, CH4{\mathrm{CH}}_{4}CH4​, H2{\mathrm{H}}_{2}H2​O, CO, N2{\mathrm{N}}_{2}N2​, Ar, and CO2{\mathrm{CO}}_{2}CO2​) together with an improved value of the 52{5}^{2}52D5/2{\mathrm{D}}_{5/2}D5/2​ radiative lifetime of t0{t}_{0}t0​=34.5\ifmmode\pm\else\textpm\fi{}3.5 s. The above quenching rate constants were then compared with classical ion-molecule collision theory. It was found that the quenching rates for molecular gases were comparable to the classical collision rates, while the rates for atomic gases were considerably lower.
We present a kinetic study of the low-lying electronically excited state of atomic calcium, Ca[4s4p(3PJ)], 1.885 eV above the 4s2(1S0) ground state. Ca(4 3P1) was generated by dye-laser pulsed excitation at λ= 657.3 nm of calcium vapour [Ca(4 3P1)â†� Ca(4 1S0)] at elevated temperatures (1000 K), in equilibrium with solid calcium, in a slow-flow system, kinetically equivalent to a static system. Following rapid Boltzmann equilibration within Ca(4 3PJ) through collisions, the forbidden time-resolved atomic resonance fluorescence at the same wavelength was monitored using boxcar integration. The decay of Ca(4 3PJ) in the presence of all the noble gases, He, Ne, Ar, Kr and Xe, was studied, yielding measurements of relative diffusion coefficients. Extrapolation of the diffusional component of the decay in each noble gas to infinite pressure yields an independent value of the mean radiative lifetime for Ca(4 3P1)→ Ca(4 1S0)+hν(λ= 657.3 nm), the average of which from the measurements in all the noble gases yields τe= 0.34 ± 0.02 ms (error 2σ). This result is compared with values reported from previous measurements, particularly atomic beams and time-resolved measurements. The kinetic analysis also gives rise to data for the collisional quenching of Ca(4 3PJ), which is found to be insignificant for most of the noble gases [kHe,Ne,Ar,Kr⩽ 4 × 10–15 cm3 molecule–1 s–1(1000 K)], in contrast to measurements from earlier work using phase-shift techniques. Xenon, however, exhibited measurable rates of collisional quenching of Ca(4 3PJ) characterised by kXe= 2.4 ± 0.3 × 10–14 cm3 molecule–1 s–1(1000 K). The time-resolved emission technique is further applied to the study of the removal of Ca(4 3PJ) by added gases, for which we report (errors 1σ)kN2=(8.9 ± 0.9)× 10–13 cm3 molecule–1 s–1(1000 K), kH2=(6.0 ± 0.6)× 10–14 cm3 molecule–1 s–1(1000 K), kD2=(2.7 ± 0.3)× 10–14 cm3 molecule–1 s–1(1000 K).
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.