Spectral decomposition at a complex laser polarization configuration

Abstract

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.

Non-linear spectral splitting of Rydberg sodium in external fields

“…It is similar to the observations for barium in a magnetic field. [24] The good agreement between the calculation and experiments also implies that there is no interference between the two channels. It is because the angular momentum projection on the magnetic axis is conservative and m is a good quantum number.…”

“…The calculation has been introduced in detail in our previous works, [20,21,24] here we only summarize the main steps. In the presence of external parallel electric and magnetic fields oriented along the z-axis, in atomic units by the convention, the non-relativistic Hamiltonian H for the Rydberg sodium atom can be written as follows: [20]…”

Nonlinear spectroscopy of barium in parallel electric and magnetic fields

“…While if the laser pulse is polarized perpendicular to the fields, both m = 1 and m = −1 states can be excited and the spectral line can be viewed as the combination of the pure m = 1 and m = −1 spectra. [14] The spectrum is recorded in the energy range including the manifolds of n = 28 and n = 29. The theoretical calculation of the spectrum lines have been convoluted with the Gaussian broadening of 0.15 cm −1 due to the laser linewidth and thermal atom Doppler broadening.…”

“…In the experiment, we use the same apparatus described previously, [14] except for an additional electric field parallel to the magnetic field. An atom beam produced from an atom oven travels to the interacting point, intersecting with the laser beam perpendicularly in the center of the superconductor magnet (Oxford Instrument).…”

“…[2] Researchers have developed a semiclassical method [7,8] and quantum calculation [9,10] to treat this problem and explain the correlative experiments. [11,12] Although there is a quadratic term in the Hamiltonian, the atom in a magnetic field has a simpler structure [13,14] than the Stark spectrum [6,15] for its higher symmetry.…”