arXiv:1906.09150 · Physical Review Letters

Precision Measurements of the Ba+138 6sS21/2−5dD25/2 Clock Transition

K. J. Arnold, R. Kaewuam, Sapam Ranjita Chanu, Ting Rei Tan, Zhiqiang Zhang, M. D. Barrett

Published May 11, 2020• 32 citations

Abstract

Measurement of the $^{138}{\mathrm{Ba}}^{+}$ ${^{2}S}_{1/2}\ensuremath{-}{^{2}D}_{5/2}$ clock transition frequency and ${D}_{5/2}$ Land\'e ${g}_{J}$ factor are reported. The clock transition frequency ${\ensuremath{\nu}}_{{\mathrm{Ba}}^{+}}=170126432449333.31\ifmmode\pm\else\textpm\fi{}(0.39{)}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}(0.29{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{Hz}$, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Land\'e ${g}_{J}$ factor for the ${^{2}D}_{5/2}$ level is determined to be ${g}_{D}=1.20036739(24)$, which is a 30-fold improvement on previous measurements. The $g$-factor measurements are corrected for an ac-magnetic field from trap-drive-induced currents in the electrodes, and data taken over a range of magnetic fields underscores the importance of accounting for this systematic.

DOI: 10.1103/physrevlett.124.193001

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arXiv:1906.09150 · Physical Review Letters

Precision Measurements of the Ba+138 6sS21/2−5dD25/2 Clock Transition

K. J. Arnold, R. Kaewuam, Sapam Ranjita Chanu, Ting Rei Tan, Zhiqiang Zhang, M. D. Barrett

Published May 11, 2020• 32 citations

arXiv HTML PDF

Abstract

Measurement of the

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

{^{2}S}_{1/2}\ensuremath{-}{^{2}D}_{5/2}

clock transition frequency and

{D}_{5/2}

Land'e

{g}_{J}

factor are reported. The clock transition frequency

{\ensuremath{\nu}}_{{\mathrm{Ba}}^{+}}=170126432449333.31\ifmmode\pm\else\textpm\fi{}(0.39{)}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}(0.29{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{Hz}

, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Land'e

{g}_{J}

factor for the

{^{2}D}_{5/2}

level is determined to be

{g}_{D}=1.20036739(24)

, which is a 30-fold improvement on previous measurements. The

g

-factor measurements are corrected for an ac-magnetic field from trap-drive-induced currents in the electrodes, and data taken over a range of magnetic fields underscores the importance of accounting for this systematic.

DOI: 10.1103/physrevlett.124.193001

Related papers

Absolute frequency measurement of the $^{40}$ Ca $^{+}$ clock transition using a GNSS link to the SI secondAbsolute frequency measurement of the $^{40}$Ca$^{+}$ clock transition using a GNSS link to the SI second

M. Guevara-Bertsch, M. K. Joshi, M. I Hussain +2 more

We report the absolute frequency measurement of the $4s$ $ ^{2}S_{1/2}\leftrightarrow 3d$ $^{2}D_{5/2}$ $^{40}$ Ca $^{+}$ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 $\times$ 10 $^{-15}$ . The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the $D_{5/2}$ sublevels and reevaluate the Landé g-factor of the $3d$ $^{2}D_{5/2}$ level to be g $_{5/2}= 1.200329(1)$ .We report the absolute frequency measurement of the $4s$ $ ^{2}S_{1/2}\leftrightarrow 3d$ $^{2}D_{5/2}$ $^{40}$Ca$^{+}$ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 $\times$ 10$^{-15}$. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the $D_{5/2}$ sublevels and reevaluate the Landé g-factor of the $3d$ $^{2}D_{5/2}$ level to be g$_{5/2}= 1.200329(1)$.

physics.atom-phCross-listedarXiv:2609.15844Sep 15, 2026

Measurement of the Landé g factor of the 5D5/2 state of Ba ii with a single trapped ion

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We present a terrestrial measurement of the Land\'e $g$ factor of the $5{D}_{5/2}$ state of singly ionized barium. Measurements were performed on single Doppler-cooled ${}^{138}{\mathrm{Ba}}^{+}$ ions in a linear Paul trap. A frequency-stabilized fiber laser with a nominal wavelength of $1.762$ $\ensuremath{\mu}$m was scanned across the $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{5/2}$ transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of $1.2020\ifmmode\pm\else\textpm\fi{}0.0005$ for ${g}_{5{D}_{5/2}}$ .We present a terrestrial measurement of the Land\'e $g$ factor of the $5{D}_{5/2}$ state of singly ionized barium. Measurements were performed on single Doppler-cooled ${}^{138}{\mathrm{Ba}}^{+}$ ions in a linear Paul trap. A frequency-stabilized fiber laser with a nominal wavelength of $1.762$ $\ensuremath{\mu}$m was scanned across the $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{5/2}$ transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of $1.2020\ifmmode\pm\else\textpm\fi{}0.0005$ for ${g}_{5{D}_{5/2}}$.

arXiv:1007.1481Physical Review ASep 27, 20106 citations

Magic wavelength of the Ba+138 6s S1/22–5d D5/22 clock transition

Sapam Ranjita Chanu, V. P. W. Koh, K. J. Arnold +5 more

The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in $^{138}\mathrm{Ba}^{+}$ has been determined to be $459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}$ . Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in $^{138}\mathrm{Ba}^{+}$ has been determined to be $459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}$. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

arXiv:1910.09736Physical Review AApr 22, 20209 citations

Measurement of the 2 S 1 / 2 − 2 D 5 / 2 clock transition in a single 171 Yb + ion

M. Roberts, P. Taylor, S. Gateva +3 more

Spectroscopy of the 411-nm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The ${}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)$ frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu} ${\mathrm{T})}^{2}$ . In addition, the hyperfine structure of the ${}^{2}{D}_{5/2}$ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The ${}^{2}{D}_{5/2}$ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.Spectroscopy of the 411-nm transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The ${}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)$ frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}${\mathrm{T})}^{2}$. In addition, the hyperfine structure of the ${}^{2}{D}_{5/2}$ level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The ${}^{2}{D}_{5/2}$ hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.

Physical Review AOct 1, 199959 citations

Radio-frequency-spectroscopy measurement of the Landé gJ factor of the 5D5/2 state of Ba + with a single trapped ion

Matthew Hoffman, Thomas W. Noel, Carolyn Auchter +4 more

We report an improved measurement of the Land\'e ${g}_{J}$ factor of the $5{D}_{5/2}$ state of singly ionized barium. Measurements were performed on single Doppler-cooled ${}^{138}$ Ba ${}^{+}$ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the $6{S}_{1/2}$ and $5{D}_{5/2}$ states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\ensuremath{\mu}$m. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e ${g}_{J}$ factor of the $6{S}_{1/2}$ state, we find a value of 1.200 372 $({4}_{\mathrm{stat}})({7}_{\mathrm{sys}})$ for ${g}_{{D}_{5/2}}$ .We report an improved measurement of the Land\'e ${g}_{J}$ factor of the $5{D}_{5/2}$ state of singly ionized barium. Measurements were performed on single Doppler-cooled ${}^{138}$Ba${}^{+}$ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the $6{S}_{1/2}$ and $5{D}_{5/2}$ states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\ensuremath{\mu}$m. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e ${g}_{J}$ factor of the $6{S}_{1/2}$ state, we find a value of 1.200 372$({4}_{\mathrm{stat}})({7}_{\mathrm{sys}})$ for ${g}_{{D}_{5/2}}$.

arXiv:1306.3518Physical Review AAug 28, 201314 citations

Polarizability assessments of ion-based optical clocks

M. D. Barrett, K. J. Arnold, Marianna S. Safronova

It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in $^{138}\mathrm{Ba}^{+}$ can be determined to an inaccuracy below $0.5%$ across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same $0.5%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with $^{138}\mathrm{Ba}^{+}$ . The approach would be equally applicable to ${\mathrm{Sr}}^{+}$ and ${\mathrm{Ca}}^{+}$ , with the latter being immediately applicable to ${\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}$ quantum logic clocks.It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in $^{138}\mathrm{Ba}^{+}$ can be determined to an inaccuracy below $0.5%$ across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same $0.5%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with $^{138}\mathrm{Ba}^{+}$. The approach would be equally applicable to ${\mathrm{Sr}}^{+}$ and ${\mathrm{Ca}}^{+}$, with the latter being immediately applicable to ${\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}$ quantum logic clocks.

arXiv:1905.04976Physical Review AOct 24, 201923 citations

Measurement of the

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

{^{2}S}_{1/2}\ensuremath{-}{^{2}D}_{5/2}

clock transition frequency and

{D}_{5/2}

Land'e

{g}_{J}

factor are reported. The clock transition frequency

{\ensuremath{\nu}}_{{\mathrm{Ba}}^{+}}=170126432449333.31\ifmmode\pm\else\textpm\fi{}(0.39{)}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}(0.29{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{Hz}

, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Land'e

{g}_{J}

factor for the

{^{2}D}_{5/2}

level is determined to be

{g}_{D}=1.20036739(24)

, which is a 30-fold improvement on previous measurements. The

g

Absolute frequency measurement of the

^{40}

^{+}

clock transition using a GNSS link to the SI second

We report the absolute frequency measurement of the

4s

$ ^{2}S_{1/2}\leftrightarrow 3d$

^{2}D_{5/2}

^{40}

^{+}

clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5

\times

^{-15}

. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the

D_{5/2}

sublevels and reevaluate the Landé g-factor of the

3d

^{2}D_{5/2}

level to be g

_{5/2}= 1.200329(1)

We present a terrestrial measurement of the Land\'e

g

factor of the

5{D}_{5/2}

state of singly ionized barium. Measurements were performed on single Doppler-cooled

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

ions in a linear Paul trap. A frequency-stabilized fiber laser with a nominal wavelength of

1.762

$\ensuremath{\mu}$m was scanned across the $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{5/2}$ transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of $1.2020\ifmmode\pm\else\textpm\fi{}0.0005$ for

{g}_{5{D}_{5/2}}

The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in

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

has been determined to be

459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}

. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

Spectroscopy of the 411-nm transition in

{}^{171}{\mathrm{Yb}}^{+}

has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The

{}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)

frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}

{\mathrm{T})}^{2}

. In addition, the hyperfine structure of the

{}^{2}{D}_{5/2}

level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The

{}^{2}{D}_{5/2}

hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.

We report an improved measurement of the Land\'e

{g}_{J}

factor of the

5{D}_{5/2}

state of singly ionized barium. Measurements were performed on single Doppler-cooled

{}^{138}

{}^{+}

ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the

6{S}_{1/2}

and

5{D}_{5/2}

states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\ensuremath{\mu}$m. By calculating the ratio of the two Zeeman splittings, and using the measured Land\'e

{g}_{J}

factor of the

6{S}_{1/2}

state, we find a value of 1.200 372

({4}_{\mathrm{stat}})({7}_{\mathrm{sys}})

for

{g}_{{D}_{5/2}}

It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in

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

can be determined to an inaccuracy below

0.5%

across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same

0.5%

level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with

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

. The approach would be equally applicable to

{\mathrm{Sr}}^{+}

and

{\mathrm{Ca}}^{+}

, with the latter being immediately applicable to

{\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}

quantum logic clocks.