Hyperfine effects on potassium tune-out wavelengths and polarizabilities

The influence of hyperfine interactions on the tune-out wavelengths of the ³⁹K, ⁴⁰K, and ⁴¹K isotopes of the potassium atom was investigated. The hyperfine interaction of the 4s_1/2 ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The 4s_1/2 state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for ³⁹K, ⁴⁰K, and ⁴¹K, respectively. The hyperfine splitting of the np_J levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the 4p_J,F states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for ³⁹K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.