Alignment in two-step pulsed laser excitation of Rydberg levels in light atoms: The example of sodium

Aligned atomic Rydberg states of sodium can be prepared using two-step excitation from the ground state by linearly polarized pulsed lasers. Information that is normally inaccessible, e.g., sublevel partial cross sections in charge-transfer experiments, can be obtained when aligned targets are used. The calculations of orbital alignment must carefully allow for fine and hyperfine structure, laser linewidths, pulse widths and delays, sublevel coherences, and other factors. In this paper we derive the orbital alignments and time-averaged d-state sublevel populations for 3 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$→3 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{\mathit{J}1}$→n ${}_{}{}^2{}_{}{}^{}$D excitations in Na using angular-momentum and density-matrix methods. We consider both quadrupole alignment ${\mathit{A}}^{\mathrm{}\left(2\right)\mathrm{}}$ and hexadecapole alignment ${\mathit{A}}^{\mathrm{}\left(4\right)\mathrm{}}$, with excitation through either ${\mathit{J}}_1$=1/2 or 3/2 intermediate states considered on the same footing. We show sublevel populations for ‖${\mathit{M}}_{\mathit{L}}$‖=0, 1, and 2 analytically and graphically. Finally, we formulate the experimental design problem quantitatively in order to ascertain how to optimize the choice of polarizer angles for extraction of sublevel partial cross sections. Although perhaps the commonest instance, two-step excitation of Na(nd) is but one of a large number of interesting cases, and this study is further intended to illustrate and guide the application of these methods to other light atoms.