Study of the velocity-selection satellites present in the 5P3/2→6PJ ( J=1/2, 3/2 ) electric quadrupole transitions in atomic rubidium

Abstract

This article presents detailed experimental and theoretical studies of the satellite fluorescence lines observed when the $5P_{3/2} \to 6P_J $, ($J = 1/2 $, $3/2$) electric quadrupole transition (E2) is excited in a room temperature vapor of rubidium atoms.
The initial state of this E2 transition is prepared by a narrow linewidth \jjm{($9 $ MHz)} laser locked to one of the dominant $5S_{1/2} \to 5P_{3/2} $ D2 hyperfine excitations for zero-velocity atoms.
Effects due to the selection of different atomic velocity classes in this preparation step are responsible for the presence of several satellite lines that can be found in the fluorescence decay spectra of both $^{85}$Rb and $^{87}$Rb.
Compared to the main lines, these satellites do not show a strong dependence on the relative linear polarization directions of the lasers used in the preparation and the electric quadrupole steps.
The relative intensities of the satellites decrease as the intensity of the preparation laser increases.
Results of a rate equation calculation that explicitly includes selection-of-velocity effects indicate that optical pumping plays a central role in determining the relative intensities and the polarization dependence of the satellite lines.
When the preparation laser is locked to the $5S_{1/2} \ F_1 = 1 \to 5P_{3/2} \ F_2 = 0$ {\it low-$F$} cyclic transition in $^{87}$Rb, six lines were found in addition to the $5P_{3/2} \ F_2 = 0 \to 6P_{3/2} \ F_3 = 2 $ lone electric quadrupole transition for zero velocity atoms.
In this case, the calculated spectrum is necessary for the correct interpretation of the experimental results, clearly indicating that optical pumping and selection of velocities are responsible for these six additional electric quadrupole lines.

The 5P3/2→6PJ(J=1/2,3/2) Electric Dipole Forbidden Transitions in Rubidium

“…For parallel polarizations, the electric quadrupole transitions must obey ∆M = ±1, while for perpendicular polarization, the selection rule is ∆M = ±2 . The top panels in Figure 3 show the spectra obtained by solving the set of velocity-dependent rate equations [9]. The excellent agreement between experiment and theory shows that the three-step description accurately reproduces the position, relative intensity and polarization dependence of the main lines and also of the velocity-dependent satellites.…”

“…Therefore, in Figure 1b their hyperfine structure is presented. For the experiments with room-temperature atoms [5][6][7][8][9], the preparation laser selects the value of the total angular momentum F 1 of the ground state. The hyperfine structure and the selection rules for electric dipole transitions determine the characteristics of the 5S → 5P 3/2 preparation step.…”

“…The populations of the magnetic sublevels of the three F 2 hyperfine states are obtained by solving the rate equations in the steady state approximation [9]. The terms required for the spectral energy density between states 5SF 1 and 5P 3/2 F 2 are expressed as the product of the laser light intensity times a Lorentzian line function [17]:…”

“…Alkali atoms, with a simple electronic structure, are naturally a good testing ground in the experimental and theoretical study of electromagnetic transitions beyond the electric dipole approximation. Examples of experiments to observe such transitions in roomtemperature or hot vapors of alkali atoms include the study of s to d excitations [1][2][3], and also of the relatively strong p to p transitions in rubidium [4][5][6][7][8][9]. There are also experiments in which electric dipole forbidden transitions were observed in cold atoms in magnetooptical traps [10][11][12].…”

“…A complete calculation was then presented in [8] to explain in detail the use of the electric quadrupole transition as a probe of the Autler-Townes effect induced by the strong mixing of states produced by the preparation step. Finally, in [9], a dynamic model that includes velocity-dependent terms in the rate equation approximation is used to reproduce the positions and intensities of the main transitions and also of the satellites that result from selection of velocity effects.…”