Physical Review A

Hyperfine structure of the 2pP122 state in Be+9

J. J. Bollinger, Joseph S. Wells, David J. Wineland, Wayne M. Itano

Published Apr 1, 1985• 55 citations

Abstract

An optical-optical double resonance technique has been used on beryllium ions stored in a Penning trap to measure the magnetic dipole hyperfine interaction constant ${A}_{\frac{1}{2}}$ of the $2p^{2}P_{\frac{1}{2}}$ level in $^{9}\mathrm{Be}^{+}$. The measured value of ${A}_{\frac{1}{2}}=\ensuremath{-}118.6(3.6)$ MHz is in good agreement with theoretical calculations. The $2p^{2}P$ fine-structure splitting and the $2s^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}2p^{2}P_{\frac{3}{2},\frac{1}{2}}$ optical transition frequencies have also been measured.

DOI: 10.1103/physreva.31.2711

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Won-Kyu Lee, Han Seb Moon, Ho Suhng Suh

Optics LettersSep 24, 200732 citations

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Shaohua Li, Yihong Li Yihong Li, Jinpeng Yuan +3 more

Chinese Optics LettersJan 1, 20183 citations

Hyperfine Structure of the 6P1/2

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Energies and hyperfine splittings of the 7D levels of atomic francium

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Hyperfine-structure investigation of highly excited D2 levels in Rb87 and Cs133 using a cw tunable dye laser in a two-step excitation scheme

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Physical Review AApr 1, 197546 citations

Measurement of the unresolved Be+9 P3/22 hyperfine splittings using quantum-interference-enhanced state-selective repump spectroscopy

David Fairbank, Alessandro L. Banducci, Robert Gunkelman +2 more

Physical Review AJan 16, 20243 citations

Physical Review A

Hyperfine structure of the 2pP122 state in Be+9

J. J. Bollinger, Joseph S. Wells, David J. Wineland, Wayne M. Itano

Published Apr 1, 1985• 55 citations

Publisher

Abstract

An optical-optical double resonance technique has been used on beryllium ions stored in a Penning trap to measure the magnetic dipole hyperfine interaction constant

{A}_{\frac{1}{2}}

of the

2p^{2}P_{\frac{1}{2}}

level in

^{9}\mathrm{Be}^{+}

. The measured value of

{A}_{\frac{1}{2}}=\ensuremath{-}118.6(3.6)

MHz is in good agreement with theoretical calculations. The

2p^{2}P

fine-structure splitting and the

2s^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}2p^{2}P_{\frac{3}{2},\frac{1}{2}}

optical transition frequencies have also been measured.

DOI: 10.1103/physreva.31.2711

Related papers

Measurement of the absolute energy level and hyperfine structure of the ^87Rb 4D_5/2 state

Won-Kyu Lee, Han Seb Moon, Ho Suhng Suh

We have measured the absolute frequency of the excited state transition 5P(3/2)-4D(5/2) in a (87)Rb atom with a femtosecond frequency comb, utilizing the recently developed spectroscopic technique of the double resonance optical pumping method. The absolute energy level of the 4D(5/2) state is determined by measuring the absolute frequency of the 5S(1/2)-5P(3/2) transition simultaneously. The hyperfine structure constants of the 4D(5/2) state are obtained by using the measured frequency. The magnetic dipole constant, A, is determined to be (-16.747+/-0.010) MHz with an uncertainty reduced 60-fold compared with a previous result. The electric quadrupole constant, B, is determined, for what is to our knowledge the first time, to be (4.149+/-0.059) MHz.We have measured the absolute frequency of the excited state transition 5P(3/2)-4D(5/2) in a (87)Rb atom with a femtosecond frequency comb, utilizing the recently developed spectroscopic technique of the double resonance optical pumping method. The absolute energy level of the 4D(5/2) state is determined by measuring the absolute frequency of the 5S(1/2)-5P(3/2) transition simultaneously. The hyperfine structure constants of the 4D(5/2) state are obtained by using the measured frequency. The magnetic dipole constant, A, is determined to be (-16.747+/-0.010) MHz with an uncertainty reduced 60-fold compared with a previous result. The electric quadrupole constant, B, is determined, for what is to our knowledge the first time, to be (4.149+/-0.059) MHz.

Optics LettersSep 24, 200732 citations

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Chinese Optics LettersJan 1, 20183 citations

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R. Alheit, X. Feng, G.Z. Li +2 more

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Journal of Modern OpticsFeb 1, 19926 citations

Energies and hyperfine splittings of the 7D levels of atomic francium

Joshua M. Grossman, R. Fliller, T. E. Mehlstäubler +4 more

We report optical double-resonance spectroscopy to locate and study the ${7D}_{3/2}$ and ${7D}_{5/2}$ levels of a sample of ${}^{210}\mathrm{Fr}$ atoms confined and cooled in a magneto-optical trap. The upper state of the ${7P}_{3/2}$ trapping transition serves as the resonant intermediate level to reach the $7D$ states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming ${B(7D}_{3/2})=0,$ the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$We report optical double-resonance spectroscopy to locate and study the ${7D}_{3/2}$ and ${7D}_{5/2}$ levels of a sample of ${}^{210}\mathrm{Fr}$ atoms confined and cooled in a magneto-optical trap. The upper state of the ${7P}_{3/2}$ trapping transition serves as the resonant intermediate level to reach the $7D$ states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming ${B(7D}_{3/2})=0,$ the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$

Physical Review AOct 12, 200031 citations

Hyperfine-structure investigation of highly excited D2 levels in Rb87 and Cs133 using a cw tunable dye laser in a two-step excitation scheme

Sune R. Svanberg, Pericles G. Tsekeris

The hyperfine structure of several highly excited $^{2}D$ states in $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ has been measured. The $D$ -state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal ${D}_{1}$ and ${D}_{2}$ lines from an rf lamp was used to excite atoms into the first excited $^{2}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$ -state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$ : For $^{87}\mathrm{Rb}$ , $|a(6^{2}D_{\frac{3}{2}})|=7.84(5)$ , $|b(6^{2}D_{\frac{3}{2}})|=0.53(6)$ ( $\frac{b}{a}>0$ ), $|a(^{2}D_{\frac{5}{2}})|=3.6(7)$ , $|a(7^{2}D_{\frac{3}{2}})|=4.53(3)$ , $|b(7^{2}D_{\frac{3}{2}})|=0.26(4)$ ( $\frac{b}{a}>0$ ), $|a(7^{2}D_{\frac{5}{2}})|=2.2(5)$ . For $^{133}\mathrm{Cs}$ , $|a(8^{2}D_{\frac{3}{2}})|=3.98(8)$ , $|a(8^{2}D_{\frac{5}{2}})|=0.9(4)$ , $|a(9^{2}D_{\frac{3}{2}})|=2.37(3)$ , $|a(9^{2}D_{\frac{5}{2}})|=0.5(2)$ , $|a(10^{2}D_{\frac{3}{2}})|=1.52(3)$ , $|a(10^{2}D_{\frac{5}{2}})|=0.4(2)$ . The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For $^{87}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for $^{87}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non- $P$ -state data.The hyperfine structure of several highly excited $^{2}D$ states in $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ has been measured. The $D$-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal ${D}_{1}$ and ${D}_{2}$ lines from an rf lamp was used to excite atoms into the first excited $^{2}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$-state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$: For $^{87}\mathrm{Rb}$, $|a(6^{2}D_{\frac{3}{2}})|=7.84(5)$, $|b(6^{2}D_{\frac{3}{2}})|=0.53(6)$ ($\frac{b}{a}>0$), $|a(^{2}D_{\frac{5}{2}})|=3.6(7)$, $|a(7^{2}D_{\frac{3}{2}})|=4.53(3)$, $|b(7^{2}D_{\frac{3}{2}})|=0.26(4)$ ($\frac{b}{a}>0$), $|a(7^{2}D_{\frac{5}{2}})|=2.2(5)$. For $^{133}\mathrm{Cs}$, $|a(8^{2}D_{\frac{3}{2}})|=3.98(8)$, $|a(8^{2}D_{\frac{5}{2}})|=0.9(4)$, $|a(9^{2}D_{\frac{3}{2}})|=2.37(3)$, $|a(9^{2}D_{\frac{5}{2}})|=0.5(2)$, $|a(10^{2}D_{\frac{3}{2}})|=1.52(3)$, $|a(10^{2}D_{\frac{5}{2}})|=0.4(2)$. The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For $^{87}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for $^{87}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-$P$-state data.

Physical Review AApr 1, 197546 citations

Measurement of the unresolved Be+9 P3/22 hyperfine splittings using quantum-interference-enhanced state-selective repump spectroscopy

David Fairbank, Alessandro L. Banducci, Robert Gunkelman +2 more

Hyperfine splittings of the $^{2}P_{3/2}$ manifold in $^{9}\mathrm{Be}^{+}$ were measured directly using a single laser-cooled ion stored in a radiofrequency Paul trap. As the hyperfine structure is unresolved beneath the natural linewidth of the transition, manipulation of the initial state, polarization, and final-state populations was used to preferentially detect scattering events through specific intermediate excited states. While quantum interference effects typically complicate the modeling of unresolved measurement lineshapes, in this work quantum interference helped to suppress extraneous scattering components. The hyperfine splittings between the $|^{2}P_{3/2},F=3\ensuremath{\rangle}$ state and the $|^{2}P_{3/2},F=2\ensuremath{\rangle}$ and $|^{2}P_{3/2},F=1\ensuremath{\rangle}$ states were measured to be $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{32}=0.801(56)$ MHz and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{31}=5.050(83)$ MHz, respectively.Hyperfine splittings of the $^{2}P_{3/2}$ manifold in $^{9}\mathrm{Be}^{+}$ were measured directly using a single laser-cooled ion stored in a radiofrequency Paul trap. As the hyperfine structure is unresolved beneath the natural linewidth of the transition, manipulation of the initial state, polarization, and final-state populations was used to preferentially detect scattering events through specific intermediate excited states. While quantum interference effects typically complicate the modeling of unresolved measurement lineshapes, in this work quantum interference helped to suppress extraneous scattering components. The hyperfine splittings between the $|^{2}P_{3/2},F=3\ensuremath{\rangle}$ state and the $|^{2}P_{3/2},F=2\ensuremath{\rangle}$ and $|^{2}P_{3/2},F=1\ensuremath{\rangle}$ states were measured to be $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{32}=0.801(56)$ MHz and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{31}=5.050(83)$ MHz, respectively.

Physical Review AJan 16, 20243 citations

An optical-optical double resonance technique has been used on beryllium ions stored in a Penning trap to measure the magnetic dipole hyperfine interaction constant

{A}_{\frac{1}{2}}

of the

2p^{2}P_{\frac{1}{2}}

level in

^{9}\mathrm{Be}^{+}

. The measured value of

{A}_{\frac{1}{2}}=\ensuremath{-}118.6(3.6)

MHz is in good agreement with theoretical calculations. The

2p^{2}P

fine-structure splitting and the

2s^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}2p^{2}P_{\frac{3}{2},\frac{1}{2}}

optical transition frequencies have also been measured.

We report optical double-resonance spectroscopy to locate and study the

{7D}_{3/2}

and

{7D}_{5/2}

levels of a sample of

{}^{210}\mathrm{Fr}

atoms confined and cooled in a magneto-optical trap. The upper state of the

{7P}_{3/2}

trapping transition serves as the resonant intermediate level to reach the

7D

states. The energy difference to the ground state is measured for the accessible levels. We measure the hyperfine splittings: $\ensuremath{\Delta}{(7D}_{3/2},F=15/2\ensuremath{\leftrightarrow}13/2)=167\ifmmode\pm\else\textpm\fi{}4 \mathrm{MHz},$ $\ensuremath{\Delta}{(7D}_{5/2},F=17/2\ensuremath{\leftrightarrow}15/2)=\ensuremath{-}117.5\ifmmode\pm\else\textpm\fi{}2.5 \mathrm{MHz},$ and $\ensuremath{\Delta}{(7D}_{5/2},F=15/2\ensuremath{\leftrightarrow}13/2)=\ensuremath{-}121\ifmmode\pm\else\textpm\fi{}4$ MHz. Extrapolating the energies of the inaccessible hyperfine levels from the hyperfine constants and assuming

{B(7D}_{3/2})=0,

the center-of-gravity energy difference to the ground state is ${E(7D}_{3/2})=24244.831\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}$ and ${E(7D}_{5/2})=24333.298\ifmmode\pm\else\textpm\fi{}0.003 {\mathrm{cm}}^{\ensuremath{-}1}.$

The hyperfine structure of several highly excited

^{2}D

states in

^{87}\mathrm{Rb}

and

^{133}\mathrm{Cs}

has been measured. The

D

-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal

{D}_{1}

and

{D}_{2}

lines from an rf lamp was used to excite atoms into the first excited

^{2}P

levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer

P

-state atoms into highly excited

D

states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants

a

and

b

: For

^{87}\mathrm{Rb}

|a(6^{2}D_{\frac{3}{2}})|=7.84(5)

|b(6^{2}D_{\frac{3}{2}})|=0.53(6)

(

\frac{b}{a}>0

|a(^{2}D_{\frac{5}{2}})|=3.6(7)

|a(7^{2}D_{\frac{3}{2}})|=4.53(3)

|b(7^{2}D_{\frac{3}{2}})|=0.26(4)

(

\frac{b}{a}>0

|a(7^{2}D_{\frac{5}{2}})|=2.2(5)

. For

^{133}\mathrm{Cs}

|a(8^{2}D_{\frac{3}{2}})|=3.98(8)

|a(8^{2}D_{\frac{5}{2}})|=0.9(4)

|a(9^{2}D_{\frac{3}{2}})|=2.37(3)

|a(9^{2}D_{\frac{5}{2}})|=0.5(2)

|a(10^{2}D_{\frac{3}{2}})|=1.52(3)

|a(10^{2}D_{\frac{5}{2}})|=0.4(2)

. The

a

factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For

^{87}\mathrm{Rb}

a comparison with a recent calculation including polarization effects is made. The

b

factors for

^{87}\mathrm{Rb}

are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-

P

-state data.

Hyperfine splittings of the

^{2}P_{3/2}

manifold in

^{9}\mathrm{Be}^{+}

were measured directly using a single laser-cooled ion stored in a radiofrequency Paul trap. As the hyperfine structure is unresolved beneath the natural linewidth of the transition, manipulation of the initial state, polarization, and final-state populations was used to preferentially detect scattering events through specific intermediate excited states. While quantum interference effects typically complicate the modeling of unresolved measurement lineshapes, in this work quantum interference helped to suppress extraneous scattering components. The hyperfine splittings between the $|^{2}P_{3/2},F=3\ensuremath{\rangle}$ state and the $|^{2}P_{3/2},F=2\ensuremath{\rangle}$ and $|^{2}P_{3/2},F=1\ensuremath{\rangle}$ states were measured to be $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{32}=0.801(56)$ MHz and $\mathrm{\ensuremath{\Delta}}{\ensuremath{\nu}}_{31}=5.050(83)$ MHz, respectively.