Physical Review Letters

Hyperfine-Induced n Mixing in High Rydberg States of Sr87

R. Beigang, W. Makat, Andre Timmermann, P. J. West

Published Aug 29, 1983• 42 citations

Abstract

The hyperfine structure of high Rydberg states of $^{87}\mathrm{Sr}$ was studied for principal quantum numbers $80<~n<~150$. The hyperfine interaction causes a strong singlet-triplet mixing between levels with the same total angular momenta $F$ but different quantum numbers $n$. Semiempirical calculations show excellent agreement with experiment.

DOI: 10.1103/physrevlett.51.771

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Physical Review Letters

Hyperfine-Induced n Mixing in High Rydberg States of Sr87

R. Beigang, W. Makat, Andre Timmermann, P. J. West

Published Aug 29, 1983• 42 citations

Publisher

Abstract

The hyperfine structure of high Rydberg states of

^{87}\mathrm{Sr}

was studied for principal quantum numbers

80<~n<~150

. The hyperfine interaction causes a strong singlet-triplet mixing between levels with the same total angular momenta

F

but different quantum numbers

n

. Semiempirical calculations show excellent agreement with experiment.

DOI: 10.1103/physrevlett.51.771

Related papers

Influence of Singlet-Triplet Mixing on the Hyperfine Structure of 5snd Rydberg States in Sr87

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A systematic study of the hyperfine structure of $5snd$ $^{1}D_{2}$ and $^{3}D_{2}$ states of $^{87}\mathrm{Sr}$ was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around $n=16$ , the hyperfine structure exhibits a marked $n$ dependence which is related to the amount of singlet-triplet mixing.A systematic study of the hyperfine structure of $5snd$ $^{1}D_{2}$ and $^{3}D_{2}$ states of $^{87}\mathrm{Sr}$ was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around $n=16$, the hyperfine structure exhibits a marked $n$ dependence which is related to the amount of singlet-triplet mixing.

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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

The hyperfine structure of high Rydberg states of

^{87}\mathrm{Sr}

was studied for principal quantum numbers

80<~n<~150

. The hyperfine interaction causes a strong singlet-triplet mixing between levels with the same total angular momenta

F

but different quantum numbers

n

. Semiempirical calculations show excellent agreement with experiment.

A systematic study of the hyperfine structure of

5snd

^{1}D_{2}

and

^{3}D_{2}

states of

^{87}\mathrm{Sr}

was carried out by Doppler-free two-photon excitation. In the region of strong singlet-triplet mixing around

n=16

, the hyperfine structure exhibits a marked

n

dependence which is related to the amount of singlet-triplet mixing.

Doppler-free two-photon spectroscopy was applied to excite hyperfine-induced transitions from the $5{s}^{2}^{1}S_{0}$ ground state to the

F=I

component of the hyperfine multiplet of the

5sns^{3}S_{1}

Rydberg series of

^{87}\mathrm{Sr}

(

n=50,\dots{},85

). The experimental data confirm the interpretation of hyperfine-induced singlet-triplet mixing which is related to the singlet-triplet energy separation.

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.

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.