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Physical Review Research

Spin selection in single-frequency two-photon excitation of alkali-metal atoms

Krishnapriya Subramonian Rajasree, Ratnesh Kumar Gupta, Vandna Gokhroo, Fam Le Kien, Thomas Nieddu, Tridib Ray, Síle Nic Chormaic, Georgiy V. Tkachenko

Published Aug 31, 2020• 11 citations
Publisher

Abstract

The authors develop a theoretical framework for spin selection in single-frequency, two-photon excitation of alkali-metal atoms, and show the polarization dependence of the two-photon transition rate using a gas of rubidium atoms under excitation by paraxial laser beams in a vapor cell or by evanescent fields near an optical nanofiber.
DOI
10.1103/physrevresearch.2.033341

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We report on an experimental test of the spin selection rule for two-photon transitions in atoms. In particular, we demonstrate that the 5S1/2→6S1/25S_{1/2}\to 6S_{1/2}5S1/2​→6S1/2​ transition rate in a rubidium gas follows a quadratic dependency on the helicity parameter linked to the polarization of the excitation light. For excitation via a single Gaussian beam or two counterpropagating beams in a hot vapor cell, the transition rate scales as the squared degree of linear polarization. The rate reaches zero when the light is circularly polarized. In contrast, when the excitation is realized via an evanescent field near an optical nanofiber, the two-photon transition cannot be completely extinguished (theoretically, not lower than 13\% of the maximum rate, under our experimental conditions) by only varying the polarization of the fiber-guided light. Our findings lead to a deeper understanding of the physics of multiphoton processes in atoms in strongly nonparaxial light.
We consider a gas of two-level atoms of two species (for example, natural Rb vapor consisting of two isotopes) in the field of laser radiation tuned close to resonance with the certain transition of a specific iostope. This radiation may turn to be rather close to a near lying transition of other isotope (within the linewidth of laser radiation), so it is necessary to take into account the possibility of excitation of other isotope in order to evaluate the enrichment degree if it is aimed at the isotope separation by means of selective excitation with subsequent chemcial reaction (in our example the rubidium hydride formation) of the excited isotope which is believed to take place at a rate much higher than that in the ground state of the atom.
An ongoing spectroscopic investigation of atomic rubidium utilizes a two-photon, single-laser excitation process. Transitions accessible with our tunable laser include 5P1/2 (F ′ ) ← 5S1/2 (F) and 5P3/2 (F ′ ) ← 5S1/2 (F). The laser is split into a pump and probe beam to allow for Doppler-free measurements of transitions between hyperfine levels. The pump and probe beams are overlapped in a counter-propagating geometry and the laser frequency scans over a transition. Absorption, fluorescence and polarization spectroscopy techniques are applied to this basic experimental setup. The temperature of the vapor cell and the power of the pump and probe beams have been varied to explore line broadening effects and signal-to-noise of each technique. This humble setup will hopefully grow into a more robust experimental arrangement in which double resonance, two-laser excitations are used to explore hyperfine state changing collisions between rubidium atoms and noble gas atoms. Rb-noble gas collisions can transfer population between hyperfine levels, such as 5P3/2 (F ′ = 3) Collision ←− 5P3/2 (F ′ = 2), and the probe beam couples 7S1/2 (F ′′ = 2) ← 5P3/2 (F ′ = 3). Polarization spectroscopy signal depends on the rate of population transfer due to the collision as well as maintaining the orientation created by the pump laser. Fluorescence spectroscopy relies only on transfer of population due to the collision. Comparison of these techniques yields information regarding the change of the magnetic sublevels, mF , during hyperfine state changing collisions.
A theoretical analysis is made of the process of isotopically selective excitation of atoms in the field of opposite waves when the compensation of the Doppler broadening is incomplete. The density matrix formalism for a homogeneous steady-state case is used to obtain expressions for the total probability of the excitation of resonating and nonresonating isotopes and for the selectivity of the process defined as the ratio of these probabilities. In some cases analytic expressions are obtained and these make it possible to determine the nature of the dependence of the total probability of the excitation and selectivity on the temperature of a vapor, buffer gas concentration, ratio of the Rabi transition frequencies, detuning from a resonance, and isotopic shifts. Numerical estimates are obtained of the atomic parameters for transitions in potassium and rubidium atoms. It is shown that the adopted method is more promising for the separation of the isotopes of alkali metals than is one-photon excitation.
Polarization rotation effects in atomic sodium vapor are studied both experimentally and theoretically. Two pulsed dye laser beams propagate collinearly through a cell containing sodium vapor. The direction of polarization of a linearly polarized dye laser beam of frequency ${\ensuremath{\omega}}_{1}$ is found to be rotated by a circularly polarized beam of frequency ${\ensuremath{\omega}}_{2}$. This rotation is due to the difference in refractive index at ${\ensuremath{\omega}}_{1}$ for right and left circularly polarized light which is produced by the circularly polarized beam. When ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ is tuned near the $3S\ensuremath{-}5S$ two-photon transition of atomic sodium, this difference is primarily due to the dispersion associated with the two-photon transition. Other sources of polarization rotation which were identified include (i) real transfers of population to excited atomic levels due to collisionally induced transitions and (ii) optically induced atomic energy-level shifts. The theory includes both the effects of two-photon dispersion and optically induced energy shifts. The application of the two-photon polarization rotation effect as a fast, optically controlled shutter or modulator and as a sensitive detection technique for two-photon spectroscopy are briefly discussed.
A compact source which produces atomic alkali-metal beams in individual hyperfine sublevels has been developed. The methods are demonstrated with 23Na^{23}\mathrm{Na}23Na atoms. Initially nearly all atoms are transferred into one hyperfine sublevel (∣F,mF〉=∣2,2〉|F, {m}_{F}〉=|2, 2〉∣F,mF​〉=∣2,2〉) by a double-resonance technique using laser optical pumping and rf transitions. Subsequently the other hyperfine sublevels can be populated selectively by an adiabatic high-frequency transition. The hyperfine sublevel populations are determined by laser-induced fluorescence spectroscopy in a magnetic field.