Physical Review A

Experimental gJ factor in the metastable 5 D3/2 level of Ba+

K. H. Knöll, G. Marx, K. Hübner, F. Schweikert, S. Ståhl, C. Weber, Günther Werth

Published Aug 1, 1996• 23 citations

Abstract

The Zeeman splitting of the metastable 5${\mathit{D}}_{3/2}$ level of $^{138}\mathrm{Ba}^{+}$ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a ${\mathit{g}}_{\mathit{J}}$ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6${\mathit{S}}_{1/2}$ ground-state ${\mathit{g}}_{\mathit{J}}$ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.1199

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

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Determination of hyperfine splittings and Landé gJ factors of 5s2S1/2 and 5p2P1/2,3/2 states of Cd+111,113 for microwave frequency standards

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

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Coherent excitation of the 6S1/2 to 5D3/2 electric-quadrupole transition in 138 Ba +

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rf Spectroscopy with a Single Ba+ Ion

Timo Koerber, M. Schacht, Kristi R. G. Hendrickson +2 more

Physical Review LettersMar 26, 200225 citations

An experimental determination of gJ(He4, 2S13)gJ(H1, 1S122)

George M. Keiser, H. G. Robinson, C. E. Johnson

Physical Review ASep 1, 197722 citations

Physical Review A

Experimental gJ factor in the metastable 5 D3/2 level of Ba+

K. H. Knöll, G. Marx, K. Hübner, F. Schweikert, S. Ståhl, C. Weber, Günther Werth

Published Aug 1, 1996• 23 citations

Publisher

Abstract

The Zeeman splitting of the metastable 5

{\mathit{D}}_{3/2}

level of

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

in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a

{\mathit{g}}_{\mathit{J}}

value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6

{\mathit{S}}_{1/2}

ground-state

{\mathit{g}}_{\mathit{J}}

factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.1199

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

Determination of hyperfine splittings and Landé gJ factors of 5s2S1/2 and 5p2P1/2,3/2 states of Cd+111,113 for microwave frequency standards

J. Z. Han, R. Si, H. R. Qin +6 more

Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e ${g}_{J}$ factors of $^{111,113}\mathrm{Cd}^{+}$ . The hyperfine splittings and Land\'e ${g}_{J}$ factors of the $5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}$ states of $^{111,113}\mathrm{Cd}^{+}$ are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{111,113}\mathrm{Cd}^{+}$ are derived based on the laser-induced fluorescence spectroscopy. The ${\mathrm{Cd}}^{+}$ ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled ${\mathrm{Ca}}^{+}$ ions. The calculated values and the derived values are cross-checked, thereby guaranteeing the reliability of our results. The results provided in this paper can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, thus further improving the stability and accuracy of the microwave frequency standards based on trapped $^{111,113}\mathrm{Cd}^{+}$ ions.Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e ${g}_{J}$ factors of $^{111,113}\mathrm{Cd}^{+}$. The hyperfine splittings and Land\'e ${g}_{J}$ factors of the $5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}$ states of $^{111,113}\mathrm{Cd}^{+}$ are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the $5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state of $^{111,113}\mathrm{Cd}^{+}$ are derived based on the laser-induced fluorescence spectroscopy. The ${\mathrm{Cd}}^{+}$ ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled ${\mathrm{Ca}}^{+}$ ions. The calculated values and the derived values are cross-checked, thereby guaranteeing the reliability of our results. The results provided in this paper can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, thus further improving the stability and accuracy of the microwave frequency standards based on trapped $^{111,113}\mathrm{Cd}^{+}$ ions.

arXiv:2201.06719Physical Review AJul 27, 20226 citations

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

Nathan Kurz, Matthew Dietrich, Gang Shu +2 more

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

Coherent excitation of the 6S1/2 to 5D3/2 electric-quadrupole transition in 138 Ba +

Adam Kleczewski, Matthew Hoffman, Jeff A. Sherman +3 more

The electric dipole-forbidden, quadrupole $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{3/2}$ transition in Ba ${}^{+}$ near 2051 nm, with a natural linewidth of 13 mHz, is attractive for potential observation of parity nonconservation, and also as a clock transition for a barium ion optical frequency standard. This transition also offers a direct means of populating the metastable $5{D}_{3/2}$ state to measure the nuclear magnetic octupole moment in the odd barium isotopes. Light from a diode-pumped, solid-state Tm,Ho:YLF laser operating at 2051 nm is used to coherently drive this transition between resolved Zeeman levels in a single trapped ${}^{138}$ Ba ${}^{+}$ ion. The frequency of the laser is stabilized to a high-finesse Fabry-P\'erot cavity at 1025 nm after being frequency doubled. Rabi oscillations on this transition indicate a laser-ion coherence time of 3 ms, most likely limited by ambient magnetic field fluctuations.The electric dipole-forbidden, quadrupole $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{3/2}$ transition in Ba${}^{+}$ near 2051 nm, with a natural linewidth of 13 mHz, is attractive for potential observation of parity nonconservation, and also as a clock transition for a barium ion optical frequency standard. This transition also offers a direct means of populating the metastable $5{D}_{3/2}$ state to measure the nuclear magnetic octupole moment in the odd barium isotopes. Light from a diode-pumped, solid-state Tm,Ho:YLF laser operating at 2051 nm is used to coherently drive this transition between resolved Zeeman levels in a single trapped ${}^{138}$Ba${}^{+}$ ion. The frequency of the laser is stabilized to a high-finesse Fabry-P\'erot cavity at 1025 nm after being frequency doubled. Rabi oscillations on this transition indicate a laser-ion coherence time of 3 ms, most likely limited by ambient magnetic field fluctuations.

arXiv:1203.1978Physical Review AApr 20, 201214 citations

rf Spectroscopy with a Single Ba+ Ion

Timo Koerber, M. Schacht, Kristi R. G. Hendrickson +2 more

We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.

Physical Review LettersMar 26, 200225 citations

An experimental determination of gJ(He4, 2S13)gJ(H1, 1S122)

George M. Keiser, H. G. Robinson, C. E. Johnson

The ratio of the ${g}_{J}$ factor of $^{4}\mathrm{He}(2^{3}S_{1})$ to that of $^{87}\mathrm{Rb}(5^{2}S_{\frac{1}{2}})$ has been measured to a fractional accuracy of \ifmmode\pm\else\textpm\fi{}5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$. The Rb atoms were optically pumped, and the $^{4}\mathrm{He}(2^{3}S_{1})$ Zeeman resonance was observed through a combination of spin-exchange collisions and spin-dependent Penning ionization. Linewidths as narrow as 220 Hz were observed for the $^{4}\mathrm{He}(2^{3}S_{1})$ Zeeman resonance. The accuracy of this experiment was limited by a systematic shift in the He ${g}_{J}$ factor that depended upon the intensity of the discharge used to excite the He atoms to the $2^{3}S_{1}$ state. Calculations indicate that transfer of coherence in spin-exchange collisions with free electrons contributes to this shift. The measured ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{87}\mathrm{Rb}, 5^{2}S_{\frac{1}{2}})}=1\ensuremath{-}46.798(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Using the previously measured ratio of the ${g}_{J}$ factors of the ground state of rubidium to the ground state of hydrogen, we determine the ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{1}\mathrm{H}, 1^{2}S_{\frac{1}{2}})}=1\ensuremath{-}23.214(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. This result agrees with recent theoretical calculations and experimental determinations using atomic-beam techniques, but disagrees with an earlier experimental determination using optical-pumping techniques.The ratio of the ${g}_{J}$ factor of $^{4}\mathrm{He}(2^{3}S_{1})$ to that of $^{87}\mathrm{Rb}(5^{2}S_{\frac{1}{2}})$ has been measured to a fractional accuracy of \ifmmode\pm\else\textpm\fi{}5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$. The Rb atoms were optically pumped, and the $^{4}\mathrm{He}(2^{3}S_{1})$ Zeeman resonance was observed through a combination of spin-exchange collisions and spin-dependent Penning ionization. Linewidths as narrow as 220 Hz were observed for the $^{4}\mathrm{He}(2^{3}S_{1})$ Zeeman resonance. The accuracy of this experiment was limited by a systematic shift in the He ${g}_{J}$ factor that depended upon the intensity of the discharge used to excite the He atoms to the $2^{3}S_{1}$ state. Calculations indicate that transfer of coherence in spin-exchange collisions with free electrons contributes to this shift. The measured ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{87}\mathrm{Rb}, 5^{2}S_{\frac{1}{2}})}=1\ensuremath{-}46.798(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Using the previously measured ratio of the ${g}_{J}$ factors of the ground state of rubidium to the ground state of hydrogen, we determine the ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{1}\mathrm{H}, 1^{2}S_{\frac{1}{2}})}=1\ensuremath{-}23.214(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. This result agrees with recent theoretical calculations and experimental determinations using atomic-beam techniques, but disagrees with an earlier experimental determination using optical-pumping techniques.

Physical Review ASep 1, 197722 citations

The Zeeman splitting of the metastable 5

{\mathit{D}}_{3/2}

level of

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

{\mathit{g}}_{\mathit{J}}

value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6

{\mathit{S}}_{1/2}

ground-state

{\mathit{g}}_{\mathit{J}}

factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.

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}}

Regarding microwave frequency standards based on trapped ions, we report on the determination of the hyperfine splittings and the Land\'e

{g}_{J}

factors of

^{111,113}\mathrm{Cd}^{+}

. The hyperfine splittings and Land\'e

{g}_{J}

factors of the

5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and

5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2,3/2}

states of

^{111,113}\mathrm{Cd}^{+}

are calculated using the multiconfiguration Dirac-Hartree-Fock scheme. Furthermore, the hyperfine splittings of the

5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}

state of

^{111,113}\mathrm{Cd}^{+}

are derived based on the laser-induced fluorescence spectroscopy. The

{\mathrm{Cd}}^{+}

ions are confined in a linear Paul trap and sympathetically cooled by laser-cooled

{\mathrm{Ca}}^{+}

ions. The calculated values and the derived values are cross-checked, thereby guaranteeing the reliability of our results. The results provided in this paper can improve the signal-to-noise ratio of the clock transition and the accuracy of the second-order Zeeman shift correction, thus further improving the stability and accuracy of the microwave frequency standards based on trapped

^{111,113}\mathrm{Cd}^{+}

ions.

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 electric dipole-forbidden, quadrupole $6{S}_{1/2}\ensuremath{\leftrightarrow}5{D}_{3/2}$ transition in Ba

{}^{+}

near 2051 nm, with a natural linewidth of 13 mHz, is attractive for potential observation of parity nonconservation, and also as a clock transition for a barium ion optical frequency standard. This transition also offers a direct means of populating the metastable

5{D}_{3/2}

state to measure the nuclear magnetic octupole moment in the odd barium isotopes. Light from a diode-pumped, solid-state Tm,Ho:YLF laser operating at 2051 nm is used to coherently drive this transition between resolved Zeeman levels in a single trapped

{}^{138}

{}^{+}

ion. The frequency of the laser is stabilized to a high-finesse Fabry-P\'erot cavity at 1025 nm after being frequency doubled. Rabi oscillations on this transition indicate a laser-ion coherence time of 3 ms, most likely limited by ambient magnetic field fluctuations.

The ratio of the

{g}_{J}

factor of

^{4}\mathrm{He}(2^{3}S_{1})

to that of

^{87}\mathrm{Rb}(5^{2}S_{\frac{1}{2}})

has been measured to a fractional accuracy of \ifmmode\pm\else\textpm\fi{}5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$. The Rb atoms were optically pumped, and the

^{4}\mathrm{He}(2^{3}S_{1})

Zeeman resonance was observed through a combination of spin-exchange collisions and spin-dependent Penning ionization. Linewidths as narrow as 220 Hz were observed for the

^{4}\mathrm{He}(2^{3}S_{1})

Zeeman resonance. The accuracy of this experiment was limited by a systematic shift in the He

{g}_{J}

factor that depended upon the intensity of the discharge used to excite the He atoms to the

2^{3}S_{1}

state. Calculations indicate that transfer of coherence in spin-exchange collisions with free electrons contributes to this shift. The measured ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{87}\mathrm{Rb}, 5^{2}S_{\frac{1}{2}})}=1\ensuremath{-}46.798(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. Using the previously measured ratio of the

{g}_{J}

factors of the ground state of rubidium to the ground state of hydrogen, we determine the ratio $\frac{{g}_{J}(^{4}\mathrm{He}, 2^{3}S_{1})}{{g}_{J}(^{1}\mathrm{H}, 1^{2}S_{\frac{1}{2}})}=1\ensuremath{-}23.214(50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. This result agrees with recent theoretical calculations and experimental determinations using atomic-beam techniques, but disagrees with an earlier experimental determination using optical-pumping techniques.