Microwave spectroscopy and multi-channel quantum defect analysis of ytterbium Rydberg states

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 $6sn\ell$ Rydberg states in $^{174}$Yb and $^{171}$Yb to include the $\ell = 3$ ($f$) and $\ell = 4$ ($g$) series. Our measurements reveal $p$-$f$ mixing in odd-parity Rydberg states of $^{171}$Yb, which we incorporate by combined MQDT models for $6snp$ and $6snf$ series. Additionally, we observe that for $\ell = 4$ 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.