Physical Review A

Diamagnetic shift and singlet-triplet mixing of 6snp Yb Rydberg states with large radial extent

Jörg Neukammer, Herbert H. Rinneberg, U. Majewski

Published Aug 1, 1984• 9 citations

Abstract

The diamagnetic shifts of the ${m}_{J}=0$ and ${m}_{J}=\ifmmode\pm\else\textpm\fi{}1$ components of $6snp ^{1}P_{1}$ ($n=40,55,70,85,100$) and $6s55p ^{3}P_{0, 1}$ Rydberg states of $^{172,\phantom{\rule{0ex}{0ex}}174}\mathrm{Yb}$ have been measured in external magnetic fields up to ≌3 kG by high-resolution three-photon spectroscopy. The diamagnetic shifts have been analyzed to yield the singlettriplet mixing due to spin-orbit interaction. At $n=40$, the singlet-triplet mixing derived from diamagnetic shifts and hyperfine-structure data are in excellent agreement.

DOI: 10.1103/physreva.30.1142

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Physical Review A

Diamagnetic shift and singlet-triplet mixing of 6snp Yb Rydberg states with large radial extent

Jörg Neukammer, Herbert H. Rinneberg, U. Majewski

Published Aug 1, 1984• 9 citations

Publisher

Abstract

The diamagnetic shifts of the

{m}_{J}=0

and

{m}_{J}=\ifmmode\pm\else\textpm\fi{}1

components of

6snp ^{1}P_{1}

(

n=40,55,70,85,100

) and

6s55p ^{3}P_{0, 1}

Rydberg states of

^{172,\phantom{\rule{0ex}{0ex}}174}\mathrm{Yb}

have been measured in external magnetic fields up to ≌3 kG by high-resolution three-photon spectroscopy. The diamagnetic shifts have been analyzed to yield the singlettriplet mixing due to spin-orbit interaction. At

n=40

, the singlet-triplet mixing derived from diamagnetic shifts and hyperfine-structure data are in excellent agreement.

DOI: 10.1103/physreva.30.1142

Related papers

High-Resolution Three-Photon Spectroscopy of 6s15pP11,3 Rydberg States of Yb

U. Majewski, Jörg Neukammer, Herbert H. Rinneberg

High-resolution three-photon laser spectroscopy has been performed for the first time to gain new spectroscopic information. Starting from the $6{s}^{2}^{1}S_{0}$ ground state of Yb, $6s15p^{1,3}P_{1}$ Rydberg states were populated by two-photon-resonant, three-photon absorption via the $6s7s^{1}S_{0}$ intermediate level. As a result of two-photon line narrowing Doppler-free spectra, showing well resolved isotope shifts and hyperfine structures, were obtained. From the hyperfine coupling constants $^{171,173}A(^{1}P_{1})$ the singlet-triplet mixing was derived.High-resolution three-photon laser spectroscopy has been performed for the first time to gain new spectroscopic information. Starting from the $6{s}^{2}^{1}S_{0}$ ground state of Yb, $6s15p^{1,3}P_{1}$ Rydberg states were populated by two-photon-resonant, three-photon absorption via the $6s7s^{1}S_{0}$ intermediate level. As a result of two-photon line narrowing Doppler-free spectra, showing well resolved isotope shifts and hyperfine structures, were obtained. From the hyperfine coupling constants $^{171,173}A(^{1}P_{1})$ the singlet-triplet mixing was derived.

Physical Review LettersOct 10, 198316 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.

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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.

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Energy-level shift of 5snsS13 Rydberg states of Sr87

R. Beigang, Andre Timmermann

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.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.

Physical Review ANov 1, 198212 citations

Observation of mixed singlet-triplet Rb2 Rydberg molecules

Fabian Böttcher, Anita Gaj, K. M. Westphal +6 more

We present high-resolution spectroscopy of ${\mathrm{Rb}}_{\text{2}}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet $s$ -wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$ -wave contribution and all orders in the relative momentum $k$ , and compare the obtained molecular binding energies to the experimental data.We present high-resolution spectroscopy of ${\mathrm{Rb}}_{\text{2}}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet $s$-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$-wave contribution and all orders in the relative momentum $k$, and compare the obtained molecular binding energies to the experimental data.

arXiv:1510.01097Physical Review AMar 21, 201659 citations

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

R. Beigang, Eckart Matthias, Andre Timmermann

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.

Physical Review LettersAug 3, 198152 citations

The diamagnetic shifts of the

{m}_{J}=0

and

{m}_{J}=\ifmmode\pm\else\textpm\fi{}1

components of

6snp ^{1}P_{1}

(

n=40,55,70,85,100

) and

6s55p ^{3}P_{0, 1}

Rydberg states of

^{172,\phantom{\rule{0ex}{0ex}}174}\mathrm{Yb}

n=40

, the singlet-triplet mixing derived from diamagnetic shifts and hyperfine-structure data are in excellent agreement.

High-resolution three-photon laser spectroscopy has been performed for the first time to gain new spectroscopic information. Starting from the $6{s}^{2}^{1}S_{0}$ ground state of Yb,

6s15p^{1,3}P_{1}

Rydberg states were populated by two-photon-resonant, three-photon absorption via the

6s7s^{1}S_{0}

intermediate level. As a result of two-photon line narrowing Doppler-free spectra, showing well resolved isotope shifts and hyperfine structures, were obtained. From the hyperfine coupling constants

^{171,173}A(^{1}P_{1})

the singlet-triplet mixing was derived.

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.

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.

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.

We present high-resolution spectroscopy of

{\mathrm{Rb}}_{\text{2}}

ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet

s

-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the

p

-wave contribution and all orders in the relative momentum

k

, and compare the obtained molecular binding energies to the experimental data.

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.