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Physical Review Applied

Determining the lifetime of the 5s5p3P0o metastable state in 87Sr from the electric dipole matrix element

Xiaotong Lu, Feng Guo, Yanyan Liu, Jingjing Xia, Guo-Dong Zhao, Ying-Xin Chen, Yebing Wang, Benquan Lu, Hong Chang

Published Feb 22, 2024• 13 citations
Publisher

Abstract

We report a measurement of the radiative lifetime of the $5s5p\phantom{\rule{0.25em}{0ex}}{}^{3}{P}_{0}^{\mathrm{o}}$ metastable state in ${}^{87}\mathrm{Sr}$, which is coupled to the $5{s}^{2}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.2em}{0ex}}{}^{1}{S}_{0}$ ground state via a hyperfine-induced electric dipole transition. The radiative lifetime is determined to be 151.4(48) s, in good agreement with theoretical results. Our approach relies on accurate measurements of laser intensity and free-space Rabi frequency, enabling lifetime measurements of any excited state and particularly suitable for long-lived states.

DOI
10.1103/physrevapplied.21.024042

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Radiative lifetime of metastable 2S13 Li+

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The radiative lifetime of $1s2s^{3}S_{1}$ ${\mathrm{Li}}^{+}$ ions has been measured by a comparison of the count rate of spontaneous decay photons (210 \AA{}) to a laser-induced fluorescence signal proportional to the total number of metastable ions. The ions were confined in a rf-quadrupole trap, and the fluorescence signal used was the intercombination transition $1s2p^{3}P_{1}$ to $1{s}^{2}^{1}S_{0}$ at 202 \AA{}. The $^{3}P_{1}$ state was populated from $^{3}S_{1}$ by absorption of laser photons at 5485 \AA{}. The result is ${\ensuremath{\tau}}_{r}=58.6\ifmmode\pm\else\textpm\fi{}12.9$ sec (95% confidence level); theory predicts ${\ensuremath{\tau}}_{r}=49.1$ sec.

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We report a measurement of the radiative lifetime of the 5s5p3P0o5s5p\phantom{\rule{0.25em}{0ex}}{}^{3}{P}_{0}^{\mathrm{o}}5s5p3P0o​ metastable state in 87Sr{}^{87}\mathrm{Sr}87Sr, which is coupled to the 5s21S05{s}^{2}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.2em}{0ex}}{}^{1}{S}_{0}5s21S0​ ground state via a hyperfine-induced electric dipole transition. The radiative lifetime is determined to be 151.4(48) s, in good agreement with theoretical results. Our approach relies on accurate measurements of laser intensity and free-space Rabi frequency, enabling lifetime measurements of any excited state and particularly suitable for long-lived states.
Lifetime Determination of the 5s5p5s5p5s5p 3P0o{}^{3}P^{\rm{o}}_{0}3P0o​ Metastable State in 87{}^{87}87Sr from the Electric Dipole Matrix Element
We report a measurement of the radiative lifetime of the 5s5p  3P0o5s5p \; {}^{\rm{3}}P^{\rm{o}}_{\rm{0}}5s5p3P0o​ metastable state in 87{}^{87}87Sr, which is coupled to the 5s2  s^{\rm{2}} \;s2 1S0{}^{\rm{1}}S_{\rm{0}}1S0​ ground state via a hyperfine-induced electric dipole transition. The radiative lifetime is determined to be 151.4(48) s, in good agreement with theoretical results. Our approach relies on accurate measurements of laser intensity and free-space Rabi frequency, enabling lifetime measurements of any excited state and particularly suitable for long-lived states.
The radiative lifetime of the 1S0{}^{1}{S}_{0}1S0​ metastable state of Xe2+{\mathrm{Xe}}^{2+}Xe2+ has been measured with a different type of electrostatic ion trap. The ion trap stores ion beams of a few keV using purely electrostatic fields and provides a large field-free region where the stored ions oscillate. A photomultiplier working in the single-photon counting mode was used to observe the 380 nm photons arising from the magnetic dipole (M1)(M1)(M1) transition ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{S}_{0}}}^{3}{P}_{1}$ of Xe2+.{\mathrm{Xe}}^{2+}.Xe2+. The present measurement yields a value of $4.46\ifmmode\pm\else\textpm\fi{}0.08 \mathrm{ms},$ which is in good agreement with previous measurements, but is almost four times more accurate.
Lifetime of the 2F7/2^2F_{7/2}2F7/2​ level in Yb+^++ for spontaneous emission of electric octupole radiation
We report a measurement of the radiative lifetime of the ^{2}F_{7/2} level of ^{171}Yb^{+} that is coupled to the ^{2}S_{1/2} ground state via an electric octupole transition. The radiative lifetime is determined to be 4.98(25)×10^{7} s, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.
We report a measurement of the radiative lifetime of the 2F7/2^{2}{F}_{7/2}2F7/2​ level of 171Yb+^{171}{\mathrm{Yb}}^{+}171Yb+ that is coupled to the 2S1/2^{2}{S}_{1/2}2S1/2​ ground state via an electric octupole transition. The radiative lifetime is determined to be $4.98(25)\ifmmode\times\else\texttimes\fi{}{10}^{7}\text{ }\text{ }\mathrm{s}$, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.
In this paper, we theoretically calculate the natural lifetime of the 5s5p3P0o5s5p\phantom{\rule{4pt}{0ex}}^{3}\mathrm{P}_{0}^{o}5s5p3P0o​ state of the 87Sr^{87}\mathrm{Sr}87Sr atom and evaluate the effect of an external magnetic field on the lifetimes of Zeeman sublevels. Using the multiconfiguration Dirac-Hartree-Fock method, the hyperfine-induced 5s5p3P0o−−5s21S05s5p^{3}\mathrm{P}_{0}^{o}--5{s}^{2}\phantom{\rule{0.28em}{0ex}}^{1}\mathrm{S}_{0}5s5p3P0o​−−5s21S0​ clock transition rate of 87Sr^{87}\mathrm{Sr}87Sr is estimated as $6.39(37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to a lifetime of 156(9) s. Our result closely agrees with previous measurements after correcting the decay rate due to the black-body radiation effect. Additionally, the transition rates of Zeeman sublevels are calculated as a function of the magnetic-field strength. Our theoretical results reveal that transition rates between different excited Zeeman states are discrepant, and the lifetime of magnetic sublevel $+{M}_{F}^{e}\phantom{\rule{4pt}{0ex}}(\ensuremath{-}{M}_{F}^{e}$; the superscript eee refers to the excited state, i.e., the 5s5p3P0o5s5p\phantom{\rule{0.28em}{0ex}}^{3}\mathrm{P}_{0}^{o}5s5p3P0o​ state) will increase (decrease) with the magnetic-field strength. Moreover, we measure the coupling strength between the clock laser and the 87Sr^{87}\mathrm{Sr}87Sr atoms, and our findings align well with theoretical estimations regarding changes in normalized coupling strength with external magnetic-field strength.
The radiative lifetime of 1s2s3S11s2s^{3}S_{1}1s2s3S1​ Li+{\mathrm{Li}}^{+}Li+ ions has been measured by a comparison of the count rate of spontaneous decay photons (210 \AA{}) to a laser-induced fluorescence signal proportional to the total number of metastable ions. The ions were confined in a rf-quadrupole trap, and the fluorescence signal used was the intercombination transition 1s2p3P11s2p^{3}P_{1}1s2p3P1​ to $1{s}^{2}^{1}S_{0}$ at 202 \AA{}. The 3P1^{3}P_{1}3P1​ state was populated from 3S1^{3}S_{1}3S1​ by absorption of laser photons at 5485 \AA{}. The result is ${\ensuremath{\tau}}_{r}=58.6\ifmmode\pm\else\textpm\fi{}12.9$ sec (95% confidence level); theory predicts ${\ensuremath{\tau}}_{r}=49.1$ sec.