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 two-photon spectroscopy was applied to investigate the msns
1S0 Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for
43Ca,
87Sr,
135Ba, and
137Ba 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.
A combined experimental and theoretical spectroscopic study of high-$n, 30\ensuremath{\lesssim}n\ensuremath{\lesssim}100$, triplet
S and
D Rydberg states in
87Sr is presented.
87Sr 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-
nS states, the hyperfine shifts are evaluated nonperturbatively, taking advantage of earlier spectroscopic data for the
I=0 isotope
88Sr, which results in good agreement with the present measurements. For the
D states, this procedure is reversed by first extracting from the present
87Sr measurements the energies of the
3D1,2,3 states to be expected for isotopes without hyperfine structure (
88Sr), which allows the determination of corrected quantum defects in the high-
n limit.
The hyperfine structure of
6snd1D2 Rydberg states of
135,137Ba 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
6snd1D2and3D2 Rydberg states in the vicinity of the
5d7d1D2 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 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
174Yb and
171Yb 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
171Yb, 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.