Electromagnetically-induced-transparency spectroscopy of high-lying Rydberg states in K39

We present a study of the Rydberg spectrum in $^{39}\mathrm{K}$ for $nS$ and $n{D}_{3/2}$ series connected to $5{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ using two-photon spectroscopy based on electromagnetically induced transparency in a heated vapor cell. We observed some 80 transitions from $5{P}_{1/2}$ to Rydberg states with principal quantum numbers $n\ensuremath{\sim}50--90$, and determined their transition frequencies and state energies with sub-GHz precision. Our spectroscopy results lay the groundwork for using Rydberg atoms as sensitive microwave photon detectors in searches for dark matter axions in the $\ensuremath{\sim}40--200 \ensuremath{\mu}\mathrm{eV}$ mass range, which is a prime range for future axion searches suggested by theory studies.