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Physical Review A

Quantum jumps and the single trapped barium ion: Determination of collisional quenching rates for the 5 d2 D5/2 level

Alan A. Madej, J. D. Sankey

Published Mar 1, 1990• 75 citations
Publisher

Abstract

A single ${\mathrm{Ba}}^{+}$ 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 $^{2}D_{5/2}$ 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 $^{2}D_{5/2}$ 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 (${\mathrm{H}}_{2}$, He, ${\mathrm{CH}}_{4}$, ${\mathrm{H}}_{2}$O, CO, ${\mathrm{N}}_{2}$, Ar, and ${\mathrm{CO}}_{2}$) together with an improved value of the ${5}^{2}$${\mathrm{D}}_{5/2}$ radiative lifetime of ${t}_{0}$=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.

DOI
10.1103/physreva.41.2621

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We report a measurement of the lifetime of the $3d{}^{2}{D}_{5/2}$ metastable level in ${}^{40}{\mathrm{Ca}}^{+},$ using quantum jumps of a single cold calcium ion in a linear Paul trap. The $4s{}^{2}{S}_{1/2}--3d{}^{2}{D}_{5/2}$ 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 $64000$ 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 $3d{}^{2}{D}_{3/2}.$ We also use quantum jump observations to demonstrate photon antibunching, and to estimate background pressure and heating rates in the ion trap.

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

Martina Knoop, M. Vedel, F. Vedel

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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Laser cooling and quantum jumps of a single indium ion

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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 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\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 {5}^{2}$${\mathrm{D}}_{5/2} 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.
A single Sr+ atom was confined in a radio-frequency quadrupole trap and laser cooled with resonant laser light. Examination of the transition Doppler profile indicated an ion kinetic temperature of less than 500 mK. Quantum jumps into and out of the metastable 4d(2)D(5/2) level were observed by laser excitation on the electric-quadrupole-allowed transition from the ground state at 674 nm. The dark and bright periods in the strong fluorescence showed variations owing to the applied driving field on the electric-quadrupole transition. These results provide an improved determination of tau = 372 +/- 25 msec for the natural metastable-state lifetime.
We report observation of laser excitation of a narrow, magnetic-dipole-allowed, infrared transition in a single trapped ion. Quantum jumps of a Ba+{\mathrm{Ba}}^{+}Ba+ atom were observed using a diode laser tuned in resonance with the excited-state 5d 2^{2}2D3/2{\mathit{D}}_{3/2}D3/2​--5d 2^{2}2D5/2{\mathit{D}}_{5/2}D5/2​ transition at 12.48 \ensuremath{\mu}m. Single-ion resonance line shapes were obtained and a transition frequency of \ensuremath{\nu}=24 012 033\ifmmode\pm\else\textpm\fi{}11 MHz was determined. Calculated quantum jump rates of the D-D transition for the applied laser spectral brightness yield agreement with experimentally observed values.
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 lifetime of the metastable 5d2 D 5/2 state has been measured for a single trapped Ba+ ion in a Paul trap in Ultra High Vacuum (UHV) in the 10−10 mbar pressure range. A total of 5046 individual periods when the ion was shelved in this state have been recorded. A preliminary value τD5/2=26.4(1.7)\tau _{D_{5/2}} = 26.4(1.7)τD5/2​​=26.4(1.7) s is obtained through extrapolation to zero residual gas pressure.
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.
We performed laser spectroscopy of In+{\mathrm{In}}^{+}In+ ions stored in a radio-frequency trap. The 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P1{\mathit{P}}_{1}P1​ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the 3^{3}3P1{\mathit{P}}_{1}P1​ state was measured using intensity modulated laser excitation: \ensuremath{\tau}(3{(}^{3}(3P1{\mathit{P}}_{1}P1​)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable 3^{3}3P0{\mathit{P}}_{0}P0​ state was populated by a magnetic dipole decay from 3^{3}3P1{\mathit{P}}_{1}P1​. The radiative lifetime of the forbidden transition 3^{3}3P0{\mathit{P}}_{0}P0​${\ensuremath{\rightarrow}}^{1}$S0{\mathit{S}}_{0}S0​ was determined from the duration of the dark periods: \ensuremath{\tau}(3{(}^{3}(3P0{\mathit{P}}_{0}P0​)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P0{\mathit{P}}_{0}P0​ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.