arXiv:1909.10516 · Physical Review A

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, Stefan Willitsch

Published Jan 14, 2020• 10 citations

Abstract

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.

DOI: 10.1103/physreva.101.012509

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arXiv:1909.10516 · Physical Review A

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, Stefan Willitsch

Published Jan 14, 2020• 10 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.101.012509

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Measurement of Dipole Matrix Elements with a Single Trapped Ion

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Hong-Fang Song, Yong-Bo Tang, Shao‐Long Chen +4 more

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.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.

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Physical Review AMar 1, 199793 citations

Measurement of the reduced dipole matrix element in Ba $^+$ Measurement of the reduced dipole matrix element in Ba$^+$

N. Jayjong, M. D. K. Lee, K. J. Arnold +1 more

We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$ . By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$ , corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$ ~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$ , we extract the static value $Δα_0(0) = -73.09(12)$ a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$, corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$, we extract the static value $Δα_0(0) = -73.09(12)$a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

physics.atom-phCross-listedarXiv:2607.20920Jul 24, 2026

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}

\ensuremath{\sigma}

{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.

<0.25%

accuracy through precision spectroscopy on an optically prepared sample of ultracold, two-level atoms. The resulting

3{}^{2}{P}_{3/2}

lifetime of 16.237(35) ns disagrees with previous time-domain measurements but is in good agreement with recent calculations and a new fast beam result.

We provide a detailed description of our fast-beam laser lifetime measurements in atomic cesium. Selective excitation of the neutral

{}^{133}\mathrm{Cs}

6p{}^{2}{P}_{1/2}

and

6p{}^{2}{P}_{3/2}

states is accomplished with resonant diode laser light directed transversely to the atomic velocity. The in-flight decay of the excited-state fluorescence is observed with a position-correlated single photon-counting detector. The Doppler-shifted

6p{}^{2}{P}_{3/2}

resonance, when probed with longitudinally propagating laser radiation, provides a precise means for determination of the beam velocity, and converts the position scale to a time scale. Our lifetime results are $35.07\ifmmode\pm\else\textpm\fi{}0.10 \mathrm{ns}$ for the

6p{}^{2}{P}_{1/2}

state and $30.57\ifmmode\pm\else\textpm\fi{}0.07 \mathrm{ns}$ for the

6p{}^{2}{P}_{3/2}

state. These results represent a data set larger than in our previous work, and include beam divergence corrections which have been evaluated by two different methods. We present comparisons of our results with previous measurements and with relativistic many-body calculations of atomic transition matrix elements in this neutral alkali system.

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.

Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of

^{39}\mathrm{K}_{2}

are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ

{\mathrm{nm}}^{3}

(-8.445(14) a.u.), \ensuremath{\tau}(4

{\mathrm{}}^{2}

{\mathrm{P}}_{3\mathrm{/}2}

)=26.34(5) ns, and \ensuremath{\tau}(4

{\mathrm{}}^{2}

{\mathrm{P}}_{1\mathrm{/}2}

)=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].

Measurement of the reduced dipole matrix element in Ba

^+

We present a high-precision measurement of the reduced electric-dipole matrix element

\langle P_{1/2}\|r\|S_{1/2}\rangle

^{138}\mathrm{Ba}^+

. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be

3.322\,7(12)

, corresponding to a

P_{1/2}

excited-state radiative lifetime of

7.866\,3(56)

~ns. Combining our experimental results with a prior model for the differential scalar polarizability

Δα_0(ω)

, we extract the static value

Δα_0(0) = -73.09(12)

a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature

\mathrm{Ba}^+

optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.