Measurements of f-, g-, and h-state quantum defects in Rydberg states of potassium

We report measurements of the quantum defects for the f, g, and h Rydberg states in potassium for principal quantum numbers $n = 26 - 29$. We made millimeter-wave measurements of the transition frequencies between $nd_j$ and the $n\ell$ states. Using the previously measured d-state quantum defects we can readily determine the $n\ell$ state quantum defects. We also report ionic dipole and quadrupole polarizabilities based on our measurements. The experiments were done in a magneto-optical trap. The cold atoms are excited to Rydberg states in steps from $4s$ to $5p$ and from $5p$ to $nd_j$ states using crossed, focussed (waist size 100 $\mu$m), lasers at 405 nm and 980 nm. Stray electric fields are nulled to less than 25 mV/cm in three dimensions using potentials applied to a set of mutually perpendicular rods surrounding the MOT cloud. Limits to the resolution of the measurements are due to the inhomogeneity of the stray fields. Our measurements of the f-state quantum defects are 5\% smaller than prior measurements and are, to the best of our knowledge, the first measurements of the g- and h-state quantum defects.