Physical Review A

Combined experimental and theoretical probe of the branching fractions of the 4P3/2 state in Ca+40

Hong-Fang Song, Yong-Bo Tang, Shao‐Long Chen, Lijun Du, Yao Huang, Hua Guan, Kelin Gao

Published Nov 14, 2019• 6 citations

Abstract

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the $4{P}_{3/2}$ state of $^{40}\mathrm{Ca}^{+}$. The measurements are based on counting photon numbers emitted from hundreds of ions trapped in a linear Paul trap, as their being affected by lasers. The calculations are performed using the relativistic coupled-cluster method at different approximations. The measured values for the decays of the $4{P}_{3/2}$ state into the $4{S}_{1/2}$, $3{D}_{5/2}$, and $3{D}_{3/2}$ states are, respectively, 0.9350(4), 0.0587(4), and 0.0063(2), which agree well with our recommended theoretical values 0.9344(13), 0.0590(12), and 0.0066(1). Our measured values are also consistent with the experimental values of Gerritsma et al. [R. Gerritsma, G. Kirchmair, F. Z\"ahringer, J. Benhelm, R. Blatt, and C. F. Roos, Eur. Phys. J. D 50, 13 (2008)] using a completely different method. Furthermore, we also calculate the branching fractions of the $4{P}_{1/2}$ state using the same method, and compare to the available experimental and theoretical data.

DOI: 10.1103/physreva.100.052505

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Physical Review A

Combined experimental and theoretical probe of the branching fractions of the 4P3/2 state in Ca+40

Hong-Fang Song, Yong-Bo Tang, Shao‐Long Chen, Lijun Du, Yao Huang, Hua Guan, Kelin Gao

Published Nov 14, 2019• 6 citations

Publisher

Abstract

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the

4{P}_{3/2}

state of

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

. The measurements are based on counting photon numbers emitted from hundreds of ions trapped in a linear Paul trap, as their being affected by lasers. The calculations are performed using the relativistic coupled-cluster method at different approximations. The measured values for the decays of the

4{P}_{3/2}

state into the

4{S}_{1/2}

3{D}_{5/2}

, and

3{D}_{3/2}

states are, respectively, 0.9350(4), 0.0587(4), and 0.0063(2), which agree well with our recommended theoretical values 0.9344(13), 0.0590(12), and 0.0066(1). Our measured values are also consistent with the experimental values of Gerritsma et al. [R. Gerritsma, G. Kirchmair, F. Z"ahringer, J. Benhelm, R. Blatt, and C. F. Roos, Eur. Phys. J. D 50, 13 (2008)] using a completely different method. Furthermore, we also calculate the branching fractions of the

4{P}_{1/2}

state using the same method, and compare to the available experimental and theoretical data.

DOI: 10.1103/physreva.100.052505

Related papers

Branching fractions for P3/2 decays in Ba+

Zhiqiang Zhang, K. J. Arnold, Sapam Ranjita Chanu +3 more

Branching fractions for decays from the ${P}_{3/2}$ level in $^{138}\mathrm{Ba}^{+}$ have been measured with a single laser-cooled ion. Decay probabilities to ${S}_{1/2}$ , ${D}_{3/2}$ , and ${D}_{5/2}$ are determined to be 0.741716(71), 0.028031(23), and 0.230253(61), respectively, which are an order-of-magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the ${D}_{5/2}$ lifetime, for which we obtain 30.14(40) s.Branching fractions for decays from the ${P}_{3/2}$ level in $^{138}\mathrm{Ba}^{+}$ have been measured with a single laser-cooled ion. Decay probabilities to ${S}_{1/2}$, ${D}_{3/2}$, and ${D}_{5/2}$ are determined to be 0.741716(71), 0.028031(23), and 0.230253(61), respectively, which are an order-of-magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the ${D}_{5/2}$ lifetime, for which we obtain 30.14(40) s.

arXiv:2003.02263Physical Review AJun 24, 202016 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

Combining experiments and relativistic theory for establishing accurate radiative quantities in atoms: The lifetime of the 2P3/2 state in Ca+40

Ziv Meir, Mudit Sinhal, Marianna S. Safronova +1 more

We report a precise determination of the lifetime of the $(4p){\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{40}\mathrm{Ca}^{+}$ , ${\ensuremath{\tau}}_{{P}_{3/2}}=6.639(42)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69(6) ns [M. S. Safronova et al., Phys. Rev. A 83, 012503 (2011)], but a 6-$\ensuremath{\sigma}$ discrepancy with the most precise previous experimental value, 6.924(19) ns [J. Jin et al., Phys. Rev. Lett. 70, 3213 (1993)], is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the ${P}_{1/2}$ state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.We report a precise determination of the lifetime of the $(4p){\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{40}\mathrm{Ca}^{+}$, ${\ensuremath{\tau}}_{{P}_{3/2}}=6.639(42)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69(6) ns [M. S. Safronova et al., Phys. Rev. A 83, 012503 (2011)], but a 6-$\ensuremath{\sigma}$ discrepancy with the most precise previous experimental value, 6.924(19) ns [J. Jin et al., Phys. Rev. Lett. 70, 3213 (1993)], is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the ${P}_{1/2}$ state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.

arXiv:1909.10516Physical Review AJan 14, 202010 citations

Measurement of the 7p2P3/2 state branching fractions in Ra+

Mingyu Fan, C. A. Holliman, S. G. Porsev +2 more

We report a measurement of the radium ion's $7p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ state branching fractions and improved theoretical calculations. With a single laser-cooled ${}^{226}{\mathrm{Ra}}^{+}$ ion we measure the ${P}_{3/2}$ branching fractions to the $7s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ ground state $0.876\phantom{\rule{0.16em}{0ex}}78(20)$ , the $6d\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}$ state $0.107\phantom{\rule{0.16em}{0ex}}59(10)$ , and the $6d\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}$ state $0.015\phantom{\rule{0.16em}{0ex}}63(21)$ .We report a measurement of the radium ion's $7p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ state branching fractions and improved theoretical calculations. With a single laser-cooled ${}^{226}{\mathrm{Ra}}^{+}$ ion we measure the ${P}_{3/2}$ branching fractions to the $7s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ ground state $0.876\phantom{\rule{0.16em}{0ex}}78(20)$, the $6d\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}$ state $0.107\phantom{\rule{0.16em}{0ex}}59(10)$, and the $6d\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}$ state $0.015\phantom{\rule{0.16em}{0ex}}63(21)$.

arXiv:1909.05871Physical Review ADec 6, 20199 citations

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

Precise determination of the quadrupole transition matrix element of Ca+40 via branching-fraction and lifetime measurements

H. Shao, Yao Huang, H. Guan +3 more

We report the experimental determination of the $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ $\ensuremath{\leftrightarrow}$ $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ quadrupole transition matrix element in $^{40}\mathrm{Ca}^{+}$ by measuring the branching fraction of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state decaying into the ground state $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and the lifetime of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52) $e{a}_{0}^{2}$ with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.We report the experimental determination of the $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ $\ensuremath{\leftrightarrow}$ $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ quadrupole transition matrix element in $^{40}\mathrm{Ca}^{+}$ by measuring the branching fraction of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state decaying into the ground state $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and the lifetime of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52) $e{a}_{0}^{2}$ with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.

arXiv:1609.04177Physical Review AMay 24, 201717 citations

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the

4{P}_{3/2}

state of

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

4{P}_{3/2}

state into the

4{S}_{1/2}

3{D}_{5/2}

, and

3{D}_{3/2}

4{P}_{1/2}

state using the same method, and compare to the available experimental and theoretical data.

Branching fractions for decays from the

{P}_{3/2}

level in

^{138}\mathrm{Ba}^{+}

have been measured with a single laser-cooled ion. Decay probabilities to

{S}_{1/2}

{D}_{3/2}

, and

{D}_{5/2}

are determined to be 0.741716(71), 0.028031(23), and 0.230253(61), respectively, which are an order-of-magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the

{D}_{5/2}

lifetime, for which we obtain 30.14(40) s.

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 report a precise determination of the lifetime of the

(4p){\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}

state of

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

, ${\ensuremath{\tau}}_{{P}_{3/2}}=6.639(42)\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69(6) ns [M. S. Safronova et al., Phys. Rev. A 83, 012503 (2011)], but a 6-$\ensuremath{\sigma}$ discrepancy with the most precise previous experimental value, 6.924(19) ns [J. Jin et al., Phys. Rev. Lett. 70, 3213 (1993)], is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduced-dipole-matrix elements are used to directly compare our result with a recent result for the

{P}_{1/2}

state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.

We report a measurement of the radium ion's

7p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}

state branching fractions and improved theoretical calculations. With a single laser-cooled

{}^{226}{\mathrm{Ra}}^{+}

ion we measure the

{P}_{3/2}

branching fractions to the

7s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}

ground state

0.876\phantom{\rule{0.16em}{0ex}}78(20)

, the

6d\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}

state

0.107\phantom{\rule{0.16em}{0ex}}59(10)

, and the

6d\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}

state

0.015\phantom{\rule{0.16em}{0ex}}63(21)

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 the experimental determination of the

4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

$\ensuremath{\leftrightarrow}$

3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

quadrupole transition matrix element in

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

by measuring the branching fraction of the

3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

state decaying into the ground state

4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and the lifetime of the

3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52)

e{a}_{0}^{2}

with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.