Non-linear spectral splitting of Rydberg sodium in external fields

We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one sigma and pi photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The sigma spectra shows a simple linear Stark effect with the applied electric field, while the pi spectra exhibits a strong non-linear dependence on the electric field. The pi transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and pi/2 proves that it can be reproduced by simple linear combination of pi and sigma components, indicating there is no interference between the pi and sigma channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel n pi, play an important role in the spectral profile.