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arXiv:1808.05987 · Physical Review A

Spectroscopy of Sr 87 triplet Rydberg states

Roger Ding, J. D. Whalen, S. K. Kanungo, T. C. Killian, F. B. Dunning, S. Yoshida, Joachim Burgdörfer

Published Oct 12, 2018• 23 citations

Abstract

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.

DOI: 10.1103/physreva.98.042505

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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-

I=9/2

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 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.

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.

By combining a recent precise measurement of the ionization energy of

{}^{87}

Rb with previous measurements of the ground-state hyperfine structure and ionization energy of

{}^{85}

Rb, an accurate value for the ${}^{85}\text{Rb}{\ensuremath{-}}^{87}\text{Rb}$ isotope shift of the 5

{}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}

ground state can be determined. In turn, comparison with additional spectroscopic data makes it possible to evaluate isotope shifts for the low-lying excited states, which are accurate in most cases to about 1 MHz. For the 5

{}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}

and 5

{}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}

states, the specific mass-shift contribution can be determined in addition to the total shift. This information is particularly useful for spectroscopic analysis of transitions to Rydberg states and for tests of atomic theory.

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.

Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in Sr 87 , we study an intrinsic Förster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials. Published by the American Physical Society 2024

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.