Millimeter-wave spectroscopy of Rydberg states in potassium

We report high-precision measurements of millimeter-wave transitions between Rydberg states in potassium. We make measurements in a magneto-optical trap with a temperature of 1-2 mK and peak atomic density of $10^9$ atoms/cm$^3$. The cold atoms are excited to Rydberg states in steps from $4s$ to $5p$ and from $5p$ to $ns$ and $nd$ states using stabilized external-cavity diode lasers at 405 nm and 980 nm. Millimeter-wave transitions are detected by selective field ionization. We null stray electric fields in three dimensions using potentials applied to a set of mutually perpendicular rods surrounding the MOT cloud. The measured frequency intervals are measured to better than a part in 10$^7$ and are then used to determine the quantum defects and absolute energies of the Rydberg states.