arXiv:2607.07929

Dual-Platform Precision Measurement of the $3^2D_{5/2}$ to $4^2S_{1/2}$ $g$-Factor Ratio in $^{40}\text{Ca}^+$

Brian J. McMahon, Vikram S. Sandhu, John M. Gray, Creston D. Herold, Christopher M. Seck, Gilles Buchs, Kenton R. Brown, Brian C. Sawyer

physics.atom-phquant-phSubmitted Jul 8, 2026• Announced Jul 10, 2026• 0 citations• Revised Sep 29, 2026 (v2)

arXiv HTML PDF

Abstract

We report precision measurements of the ratio of Landé $g$ factors between the $3^2D_{5/2}$ and $4^2S_{1/2}$ states of a single trapped $^{40}\text{Ca}^+$ ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements rely on resonant microwave excitation of magnetic sublevels and yield a ratio of $0.599~488~813~3(2)$, which is a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurements utilize optical electric quadrupole transitions and yield a concurring value of $0.599~488~813(6)$. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

Comments: 6 pages, 3 figures, 1 table

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arXiv:2607.07929

Dual-Platform Precision Measurement of the $3^2D_{5/2}$ to $4^2S_{1/2}$ $g$ -Factor Ratio in $^{40}\text{Ca}^+$ Dual-Platform Precision Measurement of the $3^2D_{5/2}$ to $4^2S_{1/2}$ $g$-Factor Ratio in $^{40}\text{Ca}^+$

Brian J. McMahon, Vikram S. Sandhu, John M. Gray, Creston D. Herold, Christopher M. Seck, Gilles Buchs, Kenton R. Brown, Brian C. Sawyer

physics.atom-phquant-phSubmitted Jul 8, 2026• Announced Jul 10, 2026• 0 citations• Revised Sep 29, 2026 (v2)

arXiv HTML PDF

Abstract

We report precision measurements of the ratio of Landé

g

factors between the

3^2D_{5/2}

and

4^2S_{1/2}

states of a single trapped

^{40}\text{Ca}^+

ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements rely on resonant microwave excitation of magnetic sublevels and yield a ratio of

0.599~488~813~3(2)

, which is a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurements utilize optical electric quadrupole transitions and yield a concurring value of

0.599~488~813(6)

. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

Comments: 6 pages, 3 figures, 1 table

Related papers

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

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

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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

Measurement of infrared magic wavelength for an all-optical trapping of $^{40}$ Ca $^{+}$ ion clockMeasurement of infrared magic wavelength for an all-optical trapping of $^{40}$Ca$^{+}$ ion clock

Yao Huang, Hua Guan, Chengbin Li +6 more

For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$ Ca $^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$ Ca $^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$ ~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$ Ca $^{+}$ optical clock.For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be $-44.32(32)$~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of $^{40}$Ca$^{+}$ optical clock.

arXiv:2202.07828Feb 16, 20221 citation

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

K. J. Arnold, R. Kaewuam, Sapam Ranjita Chanu +3 more

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.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.

arXiv:1906.09150Physical Review LettersMay 11, 202032 citations

Dual-Platform Precision Measurement of the

3^2D_{5/2}

4^2S_{1/2}

g

-Factor Ratio in

^{40}\text{Ca}^+

We report precision measurements of the ratio of Landé

g

factors between the

3^2D_{5/2}

and

4^2S_{1/2}

states of a single trapped

^{40}\text{Ca}^+

0.599~488~813~3(2)

, which is a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurements utilize optical electric quadrupole transitions and yield a concurring value of

0.599~488~813(6)

. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

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}}

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}}

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 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.

Measurement of infrared magic wavelength for an all-optical trapping of

^{40}

^{+}

ion clock

For the first time, we experimentally determine the infrared magic wavelength for the

^{40}

^{+}

4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}

electric quadrupole transition by observation of the light shift canceling in

^{40}

^{+}

optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be

-44.32(32)

~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of

^{40}

^{+}

optical clock.

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.