arXiv:physics/0311103 · Physical Review A

Lifetime measurement of the metastable 3dD5∕22 state in the Ca+40 ion using the shelving technique on a few-ion string

Peter Frøhlich Staanum, Inger S. Jensen, R. Martinussen, D. Voigt, Michael Drewsen

Published Mar 16, 2004• 35 citations

Abstract

We present a measurement of the lifetime of the metastable $3d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state in the $^{40}\mathrm{Ca}^{+}$ 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.

DOI: 10.1103/physreva.69.032503

Related papers

Experimental and theoretical study of the 3 d D 2 –level lifetimes of Ca + 40

Axel Kreuter, Christoph Becher, Gavin P. T. Lancaster +8 more

arXiv:physics/0409038Physical Review AMar 11, 2005105 citations

Lifetime measurement of the metastable 4dD5∕22 state in Sr+88 using a single trapped ion

V. Letchumanan, M. A. Wilson, Patrick Robert Gill +1 more

Physical Review AJul 13, 200539 citations

Measurement of the lifetime of the 3d2D5/2 state in 40Ca+

P. A. Barton, C. J. S. Donald, D. M. Lucas +3 more

arXiv:physics/0002026Physical Review AAug 14, 2000132 citations

Precise lifetime determination of the metastable 3d 2 D 5/2 level in Ca + by "electron shelving"

Th. Gudjons, B Hilbert, P Seibert +1 more

Europhysics Letters (EPL)Mar 10, 199623 citations

Combined experimental and theoretical probe of the lifetime of the 3d2D5/2 state in 40Ca+

Hua Guan, H. Shao, Yuan Qian +6 more

Physical Review AFeb 18, 201514 citations

Precision measurement of the 3dD3/22 –state lifetime in a single trapped Ca+40

H. Shao, Yao Huang, H. Guan +2 more

Physical Review AOct 10, 201617 citations

arXiv:physics/0311103 · Physical Review A

Lifetime measurement of the metastable 3dD5∕22 state in the Ca+40 ion using the shelving technique on a few-ion string

Peter Frøhlich Staanum, Inger S. Jensen, R. Martinussen, D. Voigt, Michael Drewsen

Published Mar 16, 2004• 35 citations

arXiv HTML PDF

Abstract

We present a measurement of the lifetime of the metastable

3d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state in the

^{40}\mathrm{Ca}^{+}

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.

DOI: 10.1103/physreva.69.032503

Related papers

Experimental and theoretical study of the 3 d D 2 –level lifetimes of Ca + 40

Axel Kreuter, Christoph Becher, Gavin P. T. Lancaster +8 more

We report measurements of the lifetimes of the $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ and $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}$ metastable states of a single laser-cooled $^{40}\mathrm{Ca}^{+}$ ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the ${D}_{5∕2}$ state or incoherent shelving in the ${D}_{3∕2}$ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the ${D}_{5∕2}$ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the ${D}_{3∕2}$ 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 [ ${D}_{3∕2}$ state: 1196(11) ms; ${D}_{5∕2}$ 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 ${\mathrm{Ba}}^{+}$ which has similar atomic structure.We report measurements of the lifetimes of the $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ and $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}$ metastable states of a single laser-cooled $^{40}\mathrm{Ca}^{+}$ ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the ${D}_{5∕2}$ state or incoherent shelving in the ${D}_{3∕2}$ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the ${D}_{5∕2}$ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the ${D}_{3∕2}$ 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 [${D}_{3∕2}$ state: 1196(11) ms; ${D}_{5∕2}$ 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 ${\mathrm{Ba}}^{+}$ which has similar atomic structure.

arXiv:physics/0409038Physical Review AMar 11, 2005105 citations

Lifetime measurement of the metastable 4dD5∕22 state in Sr+88 using a single trapped ion

V. Letchumanan, M. A. Wilson, Patrick Robert Gill +1 more

The natural lifetime of the metastable $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state in $^{88}\mathrm{Sr}^{+}$ has been measured using a single laser-cooled, trapped ion. The ion was prepared in the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.The natural lifetime of the metastable $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state in $^{88}\mathrm{Sr}^{+}$ has been measured using a single laser-cooled, trapped ion. The ion was prepared in the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the $4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.

Physical Review AJul 13, 200539 citations

Measurement of the lifetime of the 3d2D5/2 state in 40Ca+

P. A. Barton, C. J. S. Donald, D. M. Lucas +3 more

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.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.

arXiv:physics/0002026Physical Review AAug 14, 2000132 citations

Precise lifetime determination of the metastable 3d 2 D 5/2 level in Ca + by "electron shelving"

Th. Gudjons, B Hilbert, P Seibert +1 more

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.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.

Europhysics Letters (EPL)Mar 10, 199623 citations

Combined experimental and theoretical probe of the lifetime of the 3d2D5/2 state in 40Ca+

Hua Guan, H. Shao, Yuan Qian +6 more

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)].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)].

Physical Review AFeb 18, 201514 citations

Precision measurement of the 3dD3/22 –state lifetime in a single trapped Ca+40

H. Shao, Yao Huang, H. Guan +2 more

We present a high-precision measurement of the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ --state lifetime in a single trapped $^{40}\mathrm{Ca}^{+}$ . 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 $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ --state lifetime was obtained through the measurement of the spontaneous decay rate after incoherent shelving of the ion to the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ 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 $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ --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 ${S}_{ki}=7.936(26)e{a}_{0}^{2}$ , and the ratio between the lifetimes of $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}$ and $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{5/2}$ 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.We present a high-precision measurement of the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--state lifetime in a single trapped $^{40}\mathrm{Ca}^{+}$. 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 $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--state lifetime was obtained through the measurement of the spontaneous decay rate after incoherent shelving of the ion to the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ 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 $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--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 ${S}_{ki}=7.936(26)e{a}_{0}^{2}$, and the ratio between the lifetimes of $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}$ and $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{5/2}$ 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.

Physical Review AOct 10, 201617 citations

We present a measurement of the lifetime of the metastable

3d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state in the

^{40}\mathrm{Ca}^{+}

\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.

We report measurements of the lifetimes of the

3d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}

and

3d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}

metastable states of a single laser-cooled

^{40}\mathrm{Ca}^{+}

ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the

{D}_{5∕2}

state or incoherent shelving in the

{D}_{3∕2}

state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the

{D}_{5∕2}

state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the

{D}_{3∕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 [

{D}_{3∕2}

state: 1196(11) ms;

{D}_{5∕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

{\mathrm{Ba}}^{+}

which has similar atomic structure.

The natural lifetime of the metastable

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state in

^{88}\mathrm{Sr}^{+}

has been measured using a single laser-cooled, trapped ion. The ion was prepared in the

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state by laser excitation of the $5s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ quadrupole transition at 674 nm. The decay time was measured by using Dehmelt's electron shelving method to monitor the ion's electronic state. Two separate investigations were conducted under slightly different experimental conditions. 160 000 decay times from the

4d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}

state were observed in total, and two different methods for determining the statistical value of the measured lifetime have been compared. Systematic effects have also been estimated, and including these effects yields a value of $\ensuremath{\tau}=390.8(1.6)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ ($1\ensuremath{\sigma}$ uncertainty) for the natural lifetime.

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.

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)].

We present a high-precision measurement of the

3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}

--state lifetime in a single trapped

^{40}\mathrm{Ca}^{+}

. 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

3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}

--state lifetime was obtained through the measurement of the spontaneous decay rate after incoherent shelving of the ion to the

3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}

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

3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}

--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

{S}_{ki}=7.936(26)e{a}_{0}^{2}

, and the ratio between the lifetimes of

3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}

and

3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{5/2}

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.