Physical Review A

Stimulated Raman spectroscopy and the determination of the D -fine-structure level separation in C40a+

Rekishu Yamazaki, Hideyuki Sawamura, Kenji Toyoda, Shinji Urabe

Published Jan 23, 2008• 15 citations

Abstract

We describe the results of stimulated Raman spectroscopy between the fine-structure levels, specifically $3{d}^{2}{D}_{3/2}$ and $3{d}^{2}{D}_{5/2}$ metastable states, in a single trapped ${^{40}\text{C}\text{a}}^{+}$. Transitions between different Zeeman sublevels, split by an applied magnetic field, are clearly observed and the fine-structure level separation of $\ensuremath{\nu}=1\text{ }819\text{ }599\text{ }021\text{ }504\ifmmode\pm\else\textpm\fi{}37\text{ }\text{Hz}$ is determined. This measurement provides a direct observation of this level separation. From the spectroscopic data, a prospect of using the $D$-fine structure levels as a qubit for the quantum information processing is reviewed.

DOI: 10.1103/physreva.77.012508

Related papers

Measurement of the hyperfine structure of the S1∕2−D5∕2 transition in Ca+43

Jan Benhelm, Gerhard Kirchmair, Umakant D. Rapol +3 more

arXiv:physics/0611134Physical Review AMar 15, 200739 citations

Molecular-beam resonance method with Zeeman-decelerated samples: Application to metastable helium molecules

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Microwave spectroscopy and Zeeman effect of cesium ( n + 2 ) D 5 / 2 → n F J Rydberg transitions

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Physical Review AAug 1, 199623 citations

Stimulated hyper-Raman adiabatic passage. III. Experiment

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Physical Review AJul 2, 200120 citations

Physical Review A

Stimulated Raman spectroscopy and the determination of the D -fine-structure level separation in C40a+

Rekishu Yamazaki, Hideyuki Sawamura, Kenji Toyoda, Shinji Urabe

Published Jan 23, 2008• 15 citations

Publisher

Abstract

We describe the results of stimulated Raman spectroscopy between the fine-structure levels, specifically

3{d}^{2}{D}_{3/2}

and

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

metastable states, in a single trapped

{^{40}\text{C}\text{a}}^{+}

. Transitions between different Zeeman sublevels, split by an applied magnetic field, are clearly observed and the fine-structure level separation of

\ensuremath{\nu}=1\text{ }819\text{ }599\text{ }021\text{ }504\ifmmode\pm\else\textpm\fi{}37\text{ }\text{Hz}

is determined. This measurement provides a direct observation of this level separation. From the spectroscopic data, a prospect of using the

D

-fine structure levels as a qubit for the quantum information processing is reviewed.

DOI: 10.1103/physreva.77.012508

Related papers

Measurement of the hyperfine structure of the S1∕2−D5∕2 transition in Ca+43

Jan Benhelm, Gerhard Kirchmair, Umakant D. Rapol +3 more

The hyperfine structure of the $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}$ quadrupole transition at $729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in $^{43}\mathrm{Ca}^{+}$ has been investigated by laser spectroscopy using a single trapped $^{43}\mathrm{Ca}^{+}$ ion. We determine the hyperfine structure constants of the metastable level as ${A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$ and ${B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$ . The isotope shift of the transition with respect to $^{40}\mathrm{Ca}^{+}$ was measured to be ${\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between $m=0$ levels at zero magnetic field.The hyperfine structure of the $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}$ quadrupole transition at $729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in $^{43}\mathrm{Ca}^{+}$ has been investigated by laser spectroscopy using a single trapped $^{43}\mathrm{Ca}^{+}$ ion. We determine the hyperfine structure constants of the metastable level as ${A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$ and ${B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. The isotope shift of the transition with respect to $^{40}\mathrm{Ca}^{+}$ was measured to be ${\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between $m=0$ levels at zero magnetic field.

arXiv:physics/0611134Physical Review AMar 15, 200739 citations

Molecular-beam resonance method with Zeeman-decelerated samples: Application to metastable helium molecules

Luca Semeria, Paul Jansen, Gloria Clausen +3 more

We use a multistage Zeeman decelerator to generate slow beams ($v\ensuremath{\simeq}100\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}$) of translationally cold, spin-polarized metastable $a\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Sigma}}_{u}^{+}\phantom{\rule{4pt}{0ex}}{\mathrm{He}}_{2}$ molecules and perform a precision measurement of their spin-rotation fine structure. The spin polarization results from the elimination of the high-field-seeking $J=N$ spin-rotational component of each rotational level (rotational quantum number $N$ ) by the Zeeman deceleration process. By repopulating the $J=N$ component from the $J=N\ifmmode\pm\else\textpm\fi{}1$ low-field-seeking components using radio-frequency radiation, we measured the spin-rotation fine structure of 13 rovibrational levels with $v=0$ , 1 and $N=1\text{--}21$ . The low beam velocity and the resulting long interaction times with the radio-frequency radiation were exploited to determine the transition frequencies with a precision of 300 Hz.We use a multistage Zeeman decelerator to generate slow beams ($v\ensuremath{\simeq}100\phantom{\rule{0.16em}{0ex}}\mathrm{m}/\mathrm{s}$) of translationally cold, spin-polarized metastable $a\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Sigma}}_{u}^{+}\phantom{\rule{4pt}{0ex}}{\mathrm{He}}_{2}$ molecules and perform a precision measurement of their spin-rotation fine structure. The spin polarization results from the elimination of the high-field-seeking $J=N$ spin-rotational component of each rotational level (rotational quantum number $N$) by the Zeeman deceleration process. By repopulating the $J=N$ component from the $J=N\ifmmode\pm\else\textpm\fi{}1$ low-field-seeking components using radio-frequency radiation, we measured the spin-rotation fine structure of 13 rovibrational levels with $v=0$, 1 and $N=1\text{--}21$. The low beam velocity and the resulting long interaction times with the radio-frequency radiation were exploited to determine the transition frequencies with a precision of 300 Hz.

Physical Review ADec 26, 201817 citations

Microwave spectroscopy and Zeeman effect of cesium ( n + 2 ) D 5 / 2 → n F J Rydberg transitions

Jingxu Bai, Rong Song, Xijun Li +4 more

We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$ Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved $n{F}_{J}$ fine-structure levels in fields up to 120 mG, where the transition into $n{F}_{7/2}$ displays a thee-peak Zeeman pattern, while $n{F}_{5/2}$ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$ Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved $n{F}_{J}$ fine-structure levels in fields up to 120 mG, where the transition into $n{F}_{7/2}$ displays a thee-peak Zeeman pattern, while $n{F}_{5/2}$ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.

arXiv:2309.04749Physical Review AFeb 27, 20246 citations

Laser-spectroscopy measurement of the fine-structure splitting 23P1–23P2 of He4

Gaoping Feng, Xin Zheng, Yu Sun +1 more

Laser spectroscopy has been performed on a beam of neutral $^{4}\mathrm{He}$ atoms. By using transverse laser cooling and focusing, we are able to prepare a bright beam of atoms in the metastable state $2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ deflected from the original effusive atomic beam. The initial state preparation is completed with optical pumping on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transition at the wavelength of 1083 nm, followed by laser spectroscopy on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1,2}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transitions. The $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}$ fine-structure splitting is determined to be $2\phantom{\rule{0.16em}{0ex}}291\phantom{\rule{0.16em}{0ex}}177.69\ifmmode\pm\else\textpm\fi{}0.36\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The quantum interference effect is included in data extraction. This is the most precise laser spectroscopy measurement of the interval. Our result is in agreement with both the latest QED-based calculation and the most precise measurement conducted with microwave spectroscopy.Laser spectroscopy has been performed on a beam of neutral $^{4}\mathrm{He}$ atoms. By using transverse laser cooling and focusing, we are able to prepare a bright beam of atoms in the metastable state $2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ deflected from the original effusive atomic beam. The initial state preparation is completed with optical pumping on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transition at the wavelength of 1083 nm, followed by laser spectroscopy on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1,2}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transitions. The $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}$ fine-structure splitting is determined to be $2\phantom{\rule{0.16em}{0ex}}291\phantom{\rule{0.16em}{0ex}}177.69\ifmmode\pm\else\textpm\fi{}0.36\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The quantum interference effect is included in data extraction. This is the most precise laser spectroscopy measurement of the interval. Our result is in agreement with both the latest QED-based calculation and the most precise measurement conducted with microwave spectroscopy.

Physical Review AMar 23, 201524 citations

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

K. H. Knöll, G. Marx, K. Hübner +4 more

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.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.

Physical Review AAug 1, 199623 citations

Stimulated hyper-Raman adiabatic passage. III. Experiment

K. Böhmer, Thomas Halfmann, Леонід Петрович Яценко +2 more

We report the experimental realization of coherent population transfer from the $2{}^{3}S$ state to $2{}^{3}P$ fine-structure levels of helium, using the technique of hyper-Raman adiabatic passage, in which the pump-laser coupling involves a two-photon transition. We discuss the dependence of population transfer upon pump and Stokes detunings, and show that by suitably setting the detunings one can transfer population efficiently as either a two-step process to final states or as a single-step two-photon transition to an intermediate state. We use an adiabatic-state picture to interpret these experimental results. Since the optimum detuning depends on the pump laser intensity the transfer efficiency is compromised by the variation of the intensity across the spatial profile of the laser beam. Our experimental data agree well with numerical simulation based on density-matrix equations, including all 15 magnetic sublevels.We report the experimental realization of coherent population transfer from the $2{}^{3}S$ state to $2{}^{3}P$ fine-structure levels of helium, using the technique of hyper-Raman adiabatic passage, in which the pump-laser coupling involves a two-photon transition. We discuss the dependence of population transfer upon pump and Stokes detunings, and show that by suitably setting the detunings one can transfer population efficiently as either a two-step process to final states or as a single-step two-photon transition to an intermediate state. We use an adiabatic-state picture to interpret these experimental results. Since the optimum detuning depends on the pump laser intensity the transfer efficiency is compromised by the variation of the intensity across the spatial profile of the laser beam. Our experimental data agree well with numerical simulation based on density-matrix equations, including all 15 magnetic sublevels.

Physical Review AJul 2, 200120 citations

We describe the results of stimulated Raman spectroscopy between the fine-structure levels, specifically

3{d}^{2}{D}_{3/2}

and

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

metastable states, in a single trapped

{^{40}\text{C}\text{a}}^{+}

. Transitions between different Zeeman sublevels, split by an applied magnetic field, are clearly observed and the fine-structure level separation of

\ensuremath{\nu}=1\text{ }819\text{ }599\text{ }021\text{ }504\ifmmode\pm\else\textpm\fi{}37\text{ }\text{Hz}

is determined. This measurement provides a direct observation of this level separation. From the spectroscopic data, a prospect of using the

D

-fine structure levels as a qubit for the quantum information processing is reviewed.

The hyperfine structure of the $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{\ensuremath{-}}3d\phantom{\rule{0.2em}{0ex}}^{2}S_{5∕2}$ quadrupole transition at

729\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

^{43}\mathrm{Ca}^{+}

has been investigated by laser spectroscopy using a single trapped

^{43}\mathrm{Ca}^{+}

ion. We determine the hyperfine structure constants of the metastable level as

{A}_{{D}_{5∕2}}=3.8931(2)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

and

{B}_{{D}_{5∕2}}=4.241(4)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}

. The isotope shift of the transition with respect to

^{40}\mathrm{Ca}^{+}

was measured to be ${\ensuremath{\Delta}}_{\mathrm{iso}}^{43,40}=4134.713(5)\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known ``clock transitions'' between

m=0

levels at zero magnetic field.

J=N

spin-rotational component of each rotational level (rotational quantum number

N

) by the Zeeman deceleration process. By repopulating the

J=N

component from the $J=N\ifmmode\pm\else\textpm\fi{}1$ low-field-seeking components using radio-frequency radiation, we measured the spin-rotation fine structure of 13 rovibrational levels with

v=0

, 1 and

N=1\text{--}21

. The low beam velocity and the resulting long interaction times with the radio-frequency radiation were exploited to determine the transition frequencies with a precision of 300 Hz.

D

Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved

n{F}_{J}

fine-structure levels in fields up to 120 mG, where the transition into

n{F}_{7/2}

displays a thee-peak Zeeman pattern, while

n{F}_{5/2}

shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.

Laser spectroscopy has been performed on a beam of neutral

^{4}\mathrm{He}

atoms. By using transverse laser cooling and focusing, we are able to prepare a bright beam of atoms in the metastable state

2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}

deflected from the original effusive atomic beam. The initial state preparation is completed with optical pumping on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transition at the wavelength of 1083 nm, followed by laser spectroscopy on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1,2}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transitions. The $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}$ fine-structure splitting is determined to be $2\phantom{\rule{0.16em}{0ex}}291\phantom{\rule{0.16em}{0ex}}177.69\ifmmode\pm\else\textpm\fi{}0.36\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The quantum interference effect is included in data extraction. This is the most precise laser spectroscopy measurement of the interval. Our result is in agreement with both the latest QED-based calculation and the most precise measurement conducted with microwave spectroscopy.

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.

We report the experimental realization of coherent population transfer from the

2{}^{3}S

state to

2{}^{3}P

fine-structure levels of helium, using the technique of hyper-Raman adiabatic passage, in which the pump-laser coupling involves a two-photon transition. We discuss the dependence of population transfer upon pump and Stokes detunings, and show that by suitably setting the detunings one can transfer population efficiently as either a two-step process to final states or as a single-step two-photon transition to an intermediate state. We use an adiabatic-state picture to interpret these experimental results. Since the optimum detuning depends on the pump laser intensity the transfer efficiency is compromised by the variation of the intensity across the spatial profile of the laser beam. Our experimental data agree well with numerical simulation based on density-matrix equations, including all 15 magnetic sublevels.