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Physical Review Letters

Radiative Lifetime Measurement of the Ba+ Metastable D3/2 State

Nan Yu, Warren Nagourney, HANS G. DEHMELT

Published Jun 30, 1997• 65 citations
Publisher

Abstract

The extremely long lifetimes of the metastable $D$ states of the ${\mathrm{Ba}}^{+}$ 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 ${\mathrm{Ba}}^{+}$ ${D}_{3/2}$ state. We have measured the ${D}_{3/2}$ lifetime under a nearly ideal condition, i.e., single trapped ${\mathrm{Ba}}^{+}$ 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.

DOI
10.1103/physrevlett.78.4898

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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±\else\textpm\fi4.6s79.8\ifmmode\pm\else\textpm\fi{}4.6\mathrm{s}79.8\ifmmode±\else\textpm\fi4.6s 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.
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.
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 ytterbium ion has a rich level structure of low-lying states, and is one of the most widely used in experiments with trapped ions. We have measured the radiative lifetimes for the two 4f145d{4f}^{14}5d4f145d metastable states using single ytterbium ions confined in a rf trap. The obtained lifetimes for D3/2{D}_{3/2}D3/2​ and D5/2{D}_{5/2}D5/2​ states are 52.7(2.4) and 7.0(0.4) ms, respectively. The results are in good agreement with previously measured values, but differ significantly from theoretical estimates. The P1/2{P}_{1/2}P1/2​ branching ratio into D3/2{D}_{3/2}D3/2​ has also been obtained from the experiment to be 0.0483 with a 9% uncertainty.
The natural radiative lifetimes of the 5${\mathit{d}}^{9}666{\mathit{s}}^{2}$ (2{(}^{2}(2D5/2{\mathit{D}}_{5/2}D5/2​ and 2^{2}2D3/2{\mathit{D}}_{3/2}D3/2​) metastable states of Hg+{\mathrm{Hg}}^{+}Hg+ as well as of the 5${\mathit{d}}^{9}6s6s6s{(}^{3}$${\mathit{D}}_{2}$) metastable state of ${\mathrm{Hg}}^{2+}$ have been measured by counting for equal time intervals either the 282-, 198-, or 217-nm photons emitted when the respective metastable ions decay to the ground state. The metastable Hg ions are produced inside a cylindrical electrostatic ion trap by electron bombardment of background Hg vapor maintained at pressures ranging from 4 to 50\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ Torr. The trap consists of a 5.0-cm-diam, 7.5-cm-long cylinder with end caps plus a concentric 0.003-cm-diam central cylinder maintained at a negative potential of 140 V. Following electron impact of the Hg vapor, some of the photons emitted by the decaying metastable ion population are focused onto a narrow-bandwidth interference filter. The photons transmitted by the filter are detected by a photomultiplier tube as a function of time and generate a decay curve. However, the signal detected with the interference filter used to monitor the $^{2}$${\mathit{D}}_{3/2}$ metastable-state population consists of two exponentially decaying components, indicating the presence of another metastable state decaying through the emission of a photon within the bandpass of the filter. The second component is assumed to arise from a cascade originating with the 5${\mathit{d}}^{9}$6s6p (J=9/2) metastable state of Hg+{\mathrm{Hg}}^{+}Hg+. Therefore, as dictated by the composition of the photon decay curve, the pressure-dependent decay rates of the metastable states are obtained from a least-squares fit of either a single- or double-component exponential decay to the natural logarithm of the decay curve.Mean decay rates extrapolated to zero pressure of the background Hg vapor using a straight-line least-squares fit, and the inverse of the zero-pressure intercept yields the natural radiative lifetime of the relevant metastable state. Our results for the lifetimes of the 2^{2}2D5/2{\mathit{D}}_{5/2}D5/2​, 2^{2}2D3/2{\mathit{D}}_{3/2}D3/2​, and J=9/2 metastable states of Hg+{\mathrm{Hg}}^{+}Hg+ are 87\ifmmode\pm\else\textpm\fi{}4, 8.8\ifmmode\pm\else\textpm\fi{}0.4, and 60\ifmmode\pm\else\textpm\fi{}6 msec, respectively, while the lifetime of the Hg2+{\mathrm{Hg}}^{2+}Hg2+ (3{(}^{3}(3D2{\mathit{D}}_{2}D2​) metastable state is 34\ifmmode\pm\else\textpm\fi{}3 msec.
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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.