Spectral decomposition at complex laser polarization configuration

We study the role of laser polarization in the diamagnetic spectrum for the transition from the ground state to the highly excited Rydberg states through a single photon absorption. For simplicity, one usually polarizes the irradiation laser to the selected main quantum axis, which is along the applied external electric or magnetic field. The transition selection rule is simply expressed as Δm=0, which corresponds to the π transition. When the polarization is circularly polarized around the main axis, the σ⁺ or σ^- transition occurs, corresponding to the selection rule of Δm=1 or Δm=-1, respectively. A slightly more complex case is that the laser is linearly polarized perpendicular to the main axis. The numerical calculation shows that we can decompose the transition into the sum of σ⁺ and σ^- transitions, it is noted as the σ transition. For the more complex case in which the laser is linearly polarized with an arbitrary angle with respect to the main axis, we have to decompose the polarization into one along the main axis and the other one perpendicular to the main axis. They correspond to π and σ transitions, respectively. We demonstrate that these transitions in the diamagnetic spectrum and the above spectral decomposition well explain the experimentally observed spectra.