Physical Review A

Multichannel quantum-defect theory of lifetimes for highly excited states of atoms: Calculation of Yb lifetimes in the perturbed 6snd 1 ,3 D2 sequences

X. W. Liu, Z -W Wang

Published Aug 1, 1989• 15 citations

Abstract

By combining the quantum theory of radiative transition with multichannel quantum-defect theory, we have derived a general formula to calculate the lifetimes of highly excited states for atoms. As an example, we have evaluated the lifetimes for the perturbed 6snd $^{1}D_{2}$ (n=8--40) and 6snd $^{3}D_{2}$ (n=10--26) Rydberg levels, and the perturbers of the ytterbium atom. We have not only obtained results that are in perfect agreement with the recent measurements, but also predicted the lifetimes of 18 other highly excited states. The results indicate that the dramatic variation for lifetimes of Rydberg states in the vicinity of perturbing states is due to the strong channel interaction.

DOI: 10.1103/physreva.40.1838

Related papers

Natural radiative lifetime of Yb in the perturbed 6snd 1 ,3 D2 sequences

Jiang Zhankui, Chengfei Wang, Dadi Wang

Physical Review AOct 1, 19879 citations

Multichannel quantum defect theory of strontium bound Rydberg states

Christophe L. Vaillant, M P A Jones, R. M. Potvliege

arXiv:1402.5802Journal of Physics B Atomic Molecular and Optical PhysicsJul 15, 201440 citations

Lifetimes of Rydberg levels in the perturbed 6snp 3 P2 series of ytterbium i

Guo Chuan, Yingning Yu, Hua Yu +2 more

Physical Review AFeb 1, 19933 citations

Calculation of highly excited Rydberg states of ytterbium atoms

E. P. Vidolova-Angelova, Л. Н. Иванов, Vladilen S Letokhov

Journal of the Optical Society of AmericaJun 1, 198114 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

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

Physical Review A

Multichannel quantum-defect theory of lifetimes for highly excited states of atoms: Calculation of Yb lifetimes in the perturbed 6snd 1 ,3 D2 sequences

X. W. Liu, Z -W Wang

Published Aug 1, 1989• 15 citations

Publisher

Abstract

^{1}D_{2}

(n=8--40) and 6snd

^{3}D_{2}

(n=10--26) Rydberg levels, and the perturbers of the ytterbium atom. We have not only obtained results that are in perfect agreement with the recent measurements, but also predicted the lifetimes of 18 other highly excited states. The results indicate that the dramatic variation for lifetimes of Rydberg states in the vicinity of perturbing states is due to the strong channel interaction.

DOI: 10.1103/physreva.40.1838

Related papers

Natural radiative lifetime of Yb in the perturbed 6snd 1 ,3 D2 sequences

Jiang Zhankui, Chengfei Wang, Dadi Wang

Natural radiative lifetimes of ytterbium in the 6snd ${}^{1}$ ${D}_{2}$ (n=10--29), 6snd ${}^{3}$ ${D}_{2}$ (n=10--20) Rydberg sequences have been measured using stepwise excitation and a fluorescence-decay monitoring method. The lifetimes are perturbed by the 4${f}^{13}$5d6s6p configuration near n=11 and 27, except when the ${n}^{\mathrm{*}3}$ dependence of the lifetime values appeared. The lifetimes of the perturbing 5d6s6p states were also measured.Natural radiative lifetimes of ytterbium in the 6snd ${}^{1}$${D}_{2}$ (n=10--29), 6snd ${}^{3}$${D}_{2}$ (n=10--20) Rydberg sequences have been measured using stepwise excitation and a fluorescence-decay monitoring method. The lifetimes are perturbed by the 4${f}^{13}$5d6s6p configuration near n=11 and 27, except when the ${n}^{\mathrm{*}3}$ dependence of the lifetime values appeared. The lifetimes of the perturbing 5d6s6p states were also measured.

Physical Review AOct 1, 19879 citations

Multichannel quantum defect theory of strontium bound Rydberg states

Christophe L. Vaillant, M P A Jones, R. M. Potvliege

Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.

arXiv:1402.5802Journal of Physics B Atomic Molecular and Optical PhysicsJul 15, 201440 citations

Lifetimes of Rydberg levels in the perturbed 6snp 3 P2 series of ytterbium i

Guo Chuan, Yingning Yu, Hua Yu +2 more

Using three-step laser excitation in an atomic beam and a time-resolved spectroscopy technique, we measured both the lifetimes of the Rydberg levels of Yb i belonging to the perturbed series 6nsp $^{3}$ ${\mathit{P}}_{2}$ and the lifetimes of the perturbing 4${\mathit{f}}^{13} $5$ {\mathit{d}}^{2}$6s $^{3}$ ${\mathit{P}}_{2}$ ${,}^{1}$ ${\mathit{D}}_{2}$ levels. An expected shortening has been observed for the lifetimes of those levels which are strongly mixed with the perturbers.Using three-step laser excitation in an atomic beam and a time-resolved spectroscopy technique, we measured both the lifetimes of the Rydberg levels of Yb i belonging to the perturbed series 6nsp $^{3}$${\mathit{P}}_{2}$ and the lifetimes of the perturbing 4${\mathit{f}}^{13}$5${\mathit{d}}^{2}$6s $^{3}$${\mathit{P}}_{2}$${,}^{1}$${\mathit{D}}_{2}$ levels. An expected shortening has been observed for the lifetimes of those levels which are strongly mixed with the perturbers.

Physical Review AFeb 1, 19933 citations

Calculation of highly excited Rydberg states of ytterbium atoms

E. P. Vidolova-Angelova, Л. Н. Иванов, Vladilen S Letokhov

Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.

Journal of the Optical Society of AmericaJun 1, 198114 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

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

^{1}D_{2}

(n=8--40) and 6snd

^{3}D_{2}

Natural radiative lifetimes of ytterbium in the 6snd

{}^{1}

{D}_{2}

(n=10--29), 6snd

{}^{3}

{D}_{2}

(n=10--20) Rydberg sequences have been measured using stepwise excitation and a fluorescence-decay monitoring method. The lifetimes are perturbed by the 4${f}^{13}$5d6s6p configuration near n=11 and 27, except when the

{n}^{\mathrm{*}3}

dependence of the lifetime values appeared. The lifetimes of the perturbing 5d6s6p states were also measured.

Using three-step laser excitation in an atomic beam and a time-resolved spectroscopy technique, we measured both the lifetimes of the Rydberg levels of Yb i belonging to the perturbed series 6nsp

^{3}

{\mathit{P}}_{2}

and the lifetimes of the perturbing 4${\mathit{f}}^{13}

5

{\mathit{d}}^{2}$6s

^{3}

{\mathit{P}}_{2}

{,}^{1}

{\mathit{D}}_{2}

levels. An expected shortening has been observed for the lifetimes of those levels which are strongly mixed with the perturbers.

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.