Journal of Physics B Atomic Molecular and Optical Physics

Hyperfine structure of extremely high Rydberg msnd1D2,3D1,3D2and3D3series in odd alkaline-earth isotopes

Jun-Qiang Sun, K. T. Lu, R. Beigang

Published Sep 28, 1989• 13 citations

Abstract

The MQDT of hyperfine structure is greatly simplified in extremely high Rydberg states. A four (or three)-channel quantum defect model is derived for the hyperfine structure of extremely high Rydberg states of msnd configuration in odd alkaline-earth isotopes, in which the transformation matrix U i(F)i' is given analytically except for one parameter which measures the mixing of singlet 1 D 2 and triple 3 D 2 induced by spin-orbit interaction in even isotopes, and in which the four eigen quantum defects mu i' (i'=1, 2, 3, 4) are related to the quantum defects of the fine structure in even isotopes by mu i' =mod( delta i' ). This model has been used to interpret the observed sublevel structure of 5snd (n>100) configurations in 87 Sr. An excellent agreement between the theoretical and experimental results was achieved.

DOI: 10.1088/0953-4075/22/18/010

Related papers

Hyperfine structure of extremely high Rydberg msns1S0and msns3S1series in odd alkaline-earth isotopes

Jun-Qiang Sun, K. T. Lu

Journal of Physics B Atomic Molecular and Optical PhysicsJun 14, 198814 citations

Spectroscopy of Sr 87 triplet Rydberg states

Roger Ding, J. D. Whalen, S. K. Kanungo +4 more

arXiv:1808.05987Physical Review AOct 12, 201823 citations

Level shifts ofmsnsRydberg states induced by hyperfine interaction in odd alkaline-earth isotopes

R. Beigang, Andre Timmermann

Physical Review AMar 1, 198238 citations

Hyperfine structure and three-channel quantum-defect theory of 6sndD21 Rydberg states of Ba

Herbert H. Rinneberg, Jörg Neukammer

Physical Review AApr 1, 198337 citations

Configuration interaction and singlet-triplet mixing probed by hyperfine structure of 6s14d1D2and3D1,2,3barium Rydberg states

Jörg Neukammer, Herbert H. Rinneberg

The hyperfine structure of the 6s14d configuration of barium has been measured by optical-optical double resonance. From the observed positions for the hyperfine components of the 1 D 2 and 3 D 1,2,3 Rydberg states, the singlet and triplet character as well as the amount of admixture of the 5d7d perturbing configuration was deduced. Although agreeing qualitatively, the authors' results differ quantitatively from predictions made by multichannel quantum defect theory (MQDT).

Journal of Physics B Atomic and Molecular PhysicsNov 14, 198213 citations

Microwave spectroscopy and multichannel quantum defect analysis of ytterbium 6 s n p , 6 s n f , and 6 s n g Rydberg states

Rin Kuroda, Vernon M. Hughes, Martin Poitrinal +2 more

arXiv:2507.11487Physical Review ASep 16, 20252 citations

Journal of Physics B Atomic Molecular and Optical Physics

Hyperfine structure of extremely high Rydberg msnd1D2,3D1,3D2and3D3series in odd alkaline-earth isotopes

Jun-Qiang Sun, K. T. Lu, R. Beigang

Published Sep 28, 1989• 13 citations

Publisher

Abstract

DOI: 10.1088/0953-4075/22/18/010

Related papers

Hyperfine structure of extremely high Rydberg msns1S0and msns3S1series in odd alkaline-earth isotopes

Jun-Qiang Sun, K. T. Lu

In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 14, 198814 citations

Spectroscopy of Sr 87 triplet Rydberg states

Roger Ding, J. D. Whalen, S. K. Kanungo +4 more

A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet $S$ and $D$ Rydberg states in $^{87}\mathrm{Sr}$ is presented. $^{87}\mathrm{Sr}$ has a large nuclear spin $I=9/2$ , and at high- $n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high- $n S$ states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the $I=0$ isotope $^{88}\mathrm{Sr}$ , which results in good agreement with the present measurements. For the $D$ states, this procedure is reversed by first extracting from the present $^{87}\mathrm{Sr}$ measurements the energies of the ${}^{3}{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure ( $^{88}\mathrm{Sr}$ ), which allows the determination of corrected quantum defects in the high- $n$ limit.A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet $S$ and $D$ Rydberg states in $^{87}\mathrm{Sr}$ is presented. $^{87}\mathrm{Sr}$ has a large nuclear spin $I=9/2$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n S$ states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the $I=0$ isotope $^{88}\mathrm{Sr}$, which results in good agreement with the present measurements. For the $D$ states, this procedure is reversed by first extracting from the present $^{87}\mathrm{Sr}$ measurements the energies of the ${}^{3}{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure ($^{88}\mathrm{Sr}$), which allows the determination of corrected quantum defects in the high-$n$ limit.

arXiv:1808.05987Physical Review AOct 12, 201823 citations

Level shifts ofmsnsRydberg states induced by hyperfine interaction in odd alkaline-earth isotopes

R. Beigang, Andre Timmermann

High-resolution two-photon spectroscopy was applied to investigate the msns $^{1}S_{0}$ Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for $^{43}\mathrm{Ca}$ , $^{87}\mathrm{Sr}$ , $^{135}\mathrm{Ba}$ , and $^{137}\mathrm{Ba}$ that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.High-resolution two-photon spectroscopy was applied to investigate the msns $^{1}S_{0}$ Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for $^{43}\mathrm{Ca}$, $^{87}\mathrm{Sr}$, $^{135}\mathrm{Ba}$, and $^{137}\mathrm{Ba}$ that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.

Physical Review AMar 1, 198238 citations

Hyperfine structure and three-channel quantum-defect theory of 6sndD21 Rydberg states of Ba

Herbert H. Rinneberg, Jörg Neukammer

The hyperfine structure of $6snd^{1}D_{2}$ Rydberg states of $^{135,137}\mathrm{Ba}$ is reported for principal quantum numbers ranging between $n=10$ and $n=50$ . From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of $6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}$ Rydberg states in the vicinity of the $5d7d^{1}D_{2}$ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.The hyperfine structure of $6snd^{1}D_{2}$ Rydberg states of $^{135,137}\mathrm{Ba}$ is reported for principal quantum numbers ranging between $n=10$ and $n=50$. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of $6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}$ Rydberg states in the vicinity of the $5d7d^{1}D_{2}$ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

Physical Review AApr 1, 198337 citations

Configuration interaction and singlet-triplet mixing probed by hyperfine structure of 6s14d1D2and3D1,2,3barium Rydberg states

Jörg Neukammer, Herbert H. Rinneberg

Journal of Physics B Atomic and Molecular PhysicsNov 14, 198213 citations

Microwave spectroscopy and multichannel quantum defect analysis of ytterbium 6 s n p , 6 s n f , and 6 s n g Rydberg states

Rin Kuroda, Vernon M. Hughes, Martin Poitrinal +2 more

The complex Rydberg structure of ytterbium atoms is shaped by multiple low-lying ion-core-excited states and strong channel interactions, which presents both opportunities and challenges for quantum information processing and precision metrology. In this work, we extend high-resolution microwave spectroscopy and multichannel quantum defect theory (MQDT) modeling of singly excited $6sn\ensuremath{\ell}$ Rydberg states in $^{174}\mathrm{Yb}$ and $^{171}\mathrm{Yb}$ to include the $\ensuremath{\ell}=3$ ( $f$ ) and $\ensuremath{\ell}=4$ ( $g$ ) series. Our measurements reveal $p\text{\ensuremath{-}}f$ mixing in odd-parity Rydberg states of $^{171}\mathrm{Yb}$ , which we incorporate by combined MQDT models for $6snp$ and $6snf$ series. Additionally, we observe that for $\ensuremath{\ell}=4$ the spin-orbit interaction dominates over the exchange interaction, such that the $6sng$ states are more accurately described in a $jj$ -coupled basis. We validate our models by comparing the predicted Land\'e $g$ factors and static dipole polarizabilities with experimental measurements, finding excellent agreement. These results provide important input for designing high-fidelity entangling gates with ytterbium atoms.The complex Rydberg structure of ytterbium atoms is shaped by multiple low-lying ion-core-excited states and strong channel interactions, which presents both opportunities and challenges for quantum information processing and precision metrology. In this work, we extend high-resolution microwave spectroscopy and multichannel quantum defect theory (MQDT) modeling of singly excited $6sn\ensuremath{\ell}$ Rydberg states in $^{174}\mathrm{Yb}$ and $^{171}\mathrm{Yb}$ to include the $\ensuremath{\ell}=3$ ($f$) and $\ensuremath{\ell}=4$ ($g$) series. Our measurements reveal $p\text{\ensuremath{-}}f$ mixing in odd-parity Rydberg states of $^{171}\mathrm{Yb}$, which we incorporate by combined MQDT models for $6snp$ and $6snf$ series. Additionally, we observe that for $\ensuremath{\ell}=4$ the spin-orbit interaction dominates over the exchange interaction, such that the $6sng$ states are more accurately described in a $jj$-coupled basis. We validate our models by comparing the predicted Land\'e $g$ factors and static dipole polarizabilities with experimental measurements, finding excellent agreement. These results provide important input for designing high-fidelity entangling gates with ytterbium atoms.

arXiv:2507.11487Physical Review ASep 16, 20252 citations

A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet

S

and

D

Rydberg states in

^{87}\mathrm{Sr}

is presented.

^{87}\mathrm{Sr}

has a large nuclear spin

I=9/2

, and at high-

n

the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings, which poses a considerable challenge both for precision spectroscopy and for theory. For high-

n S

states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the

I=0

isotope

^{88}\mathrm{Sr}

, which results in good agreement with the present measurements. For the

D

states, this procedure is reversed by first extracting from the present

^{87}\mathrm{Sr}

measurements the energies of the

{}^{3}{D}_{1,2,3}

states to be expected for isotopes without hyperfine structure (

^{88}\mathrm{Sr}

), which allows the determination of corrected quantum defects in the high-

n

limit.

High-resolution two-photon spectroscopy was applied to investigate the msns

^{1}S_{0}

Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for

^{43}\mathrm{Ca}

^{87}\mathrm{Sr}

^{135}\mathrm{Ba}

, and

^{137}\mathrm{Ba}

that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.

The hyperfine structure of

6snd^{1}D_{2}

Rydberg states of

^{135,137}\mathrm{Ba}

is reported for principal quantum numbers ranging between

n=10

and

n=50

. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of

6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}

Rydberg states in the vicinity of the

5d7d^{1}D_{2}

perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

^{174}\mathrm{Yb}

and

^{171}\mathrm{Yb}

to include the $\ensuremath{\ell}=3$ (

f

) and $\ensuremath{\ell}=4$ (

g

) series. Our measurements reveal $p\text{\ensuremath{-}}f$ mixing in odd-parity Rydberg states of

^{171}\mathrm{Yb}

, which we incorporate by combined MQDT models for

6snp

and

6snf

series. Additionally, we observe that for $\ensuremath{\ell}=4$ the spin-orbit interaction dominates over the exchange interaction, such that the

6sng

states are more accurately described in a

jj

-coupled basis. We validate our models by comparing the predicted Land\'e

g

factors and static dipole polarizabilities with experimental measurements, finding excellent agreement. These results provide important input for designing high-fidelity entangling gates with ytterbium atoms.