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 σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π 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 π/2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel np, play an important role in the spectral profile.