Polarization spectroscopy and laser-locking for excitation of ultracold potassium atoms

We report on the use of polarization spectroscopy to lock the frequency of an external-cavity diode laser to a the 4s - 4p$_{1/2}$ (770 nm), 4s - 4p$_{3/2}$ (767 nm) and 4s - 5p$_{1/2}$ and 4s - 5p$_{3/2}$ (405 nm) transitions in potassium. A rate equation model is in good agreement with the observed lineshapes and the D2 transition lineshapes agree with prior experiments. We have used the dispersion shaped lines to lock the frequency of lasers for probing a magneto-optical trap's density on the D1 line and for stepwise excitation of potassium Rydberg states using the 4s - 5p$_{3/2}$ transition. The technique has proven particularly helpful by enabling modulation-free locking of blue diode lasers.