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Physical Review A

Pumping efficiency in an optically pumped rubidium beam with σ+π linearly polarized counterpropagating lasers

Jin Woo Jun, Ho Seong Lee

Published Nov 1, 1998• 4 citations
Publisher

Abstract

We investigate the population differences between ground-state hyperfine levels (${5S}_{1/2},F=2$ and ${5S}_{1/2},$ $F=1$) of an optically pumped ${}^{87}\mathrm{Rb}$ beam in a static magnetic field, taking into account the various kinds of atomic coherence (Zeeman, hyperfine, and optical). The pumping lasers are monochromatic and in resonance with the ${(5S}_{1/2},F=1\ensuremath{\leftrightarrow}{5P}_{1/2}{,F}^{\ensuremath{'}}=1)$ transition. By varying the polarization configuration of the pumping lasers, we find that the pumping efficiency is substantially enhanced when a $\ensuremath{\sigma}$-polarized laser and a $\ensuremath{\pi}$-polarized laser are counterpropagating. In this case, the pumping efficiency remains high even in a weak magnetic field, which explains qualitatively experimental data reported previously from a cesium beam experiment.

DOI
10.1103/physreva.58.4095

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We investigate the population differences between ground-state hyperfine levels (5S1/2,F=2{5S}_{1/2},F=25S1/2​,F=2 and 5S1/2,{5S}_{1/2},5S1/2​, F=1F=1F=1) of an optically pumped 87Rb{}^{87}\mathrm{Rb}87Rb beam in a static magnetic field, taking into account the various kinds of atomic coherence (Zeeman, hyperfine, and optical). The pumping lasers are monochromatic and in resonance with the (5S1/2,F=1\ensuremath↔5P1/2,F\ensuremath′=1){(5S}_{1/2},F=1\ensuremath{\leftrightarrow}{5P}_{1/2}{,F}^{\ensuremath{'}}=1)(5S1/2​,F=1\ensuremath↔5P1/2​,F\ensuremath′=1) transition. By varying the polarization configuration of the pumping lasers, we find that the pumping efficiency is substantially enhanced when a \ensuremathσ\ensuremath{\sigma}\ensuremathσ-polarized laser and a \ensuremathπ\ensuremath{\pi}\ensuremathπ-polarized laser are counterpropagating. In this case, the pumping efficiency remains high even in a weak magnetic field, which explains qualitatively experimental data reported previously from a cesium beam experiment.
The evolution of the hyperfine structure magnetic sublevel populations of 87 Rb and 133 Cs atoms in resonant linearly polarized laser fields is theoretically analyzed. Analytical expressions are obtained for stationary populations of the magnetic sublevels of the ground state 5 2 S 1/2 F g = 1, F f = 2 in 87 Rb and 6 2 S 1/2 F g = 3, F f = 4 in 133 Cs under optical pumping at the F g ↔ F e = F g and F f ↔ F e = F f transitions of the D 2 lines ( n 2 S 1/2 n 2 P 3/2 ) versus the initial populations. The characteristic population stabilization time are obtained by numerical solution for the density matrix equations, depending on the intensity of the laser fields and the detuning of the optical resonance. It is shown that the alternation of the polarization direction of the laser field at the transition F f ↔ F e = F f almost completely transfers atoms to the lower sublevel of the "clock" M1 transition F g M = 0 ↔ F f M = 0 in rubidium and cesium frequency standards, which proportionally increases the signal of the recording system.
Subnatural-width resonances due to coherent effects in optical pumping at hyperfine (hf) transitions of Rb are investigated using a linearly or circularly polarized single-frequency diode laser beam. The sign and amplitude of the resonances in the fluorescence are measured by scanning the laser frequency over the hf transitions of the Rb D 1 and D 2 lines. The fluorescence perpendicular to the laser beam is detected as a function of magnetic field parallel to the beam propagation and scanned around zero value. In the case of linear polarization of the field, dark resonances are observed for hf transitions with F g → F e = F g -1 and F g → F e = F g , and bright resonances are observed for transitions with F g → F e = F g + 1. This is in agreement with the recently developed theories. For all (except F g = 2→ F e = 3, 85 Rb, D 1 line) hf transitions the sign of the resonances reverses when the polarization of the field changes to circular. The amplitudes of the resonances correspond to the probability of the hf transitions and to the calculated loss rate of the population to the ground hf level not excited by the laser field. The observed narrow resonances (FWHM: few tens of kHz) and their sensitivity to weak magnetic fields are interesting for high-resolution spectroscopy and for development of simple and precise magnetometers.
We have experimentally and theoretically investigated the behavior of Na atoms under the combined influence of resonant laser light and a magnetic field. Linearly polarized light was tuned to the (3s) 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​ (F=2)\ensuremath{\rightarrow}(3p) 2{\mathrm{}}^{2}2P1/2{P}_{1/2}P1/2​ (F'=1) component of the D1{D}_{1}D1​ line. The intensity of fluorescent light was observed as a function of the laser intensity for various strengths of the magnetic field B. Trapping in the MF{M}_{F}MF​=\ifmmode\pm\else\textpm\fi{}2 levels of the ground state could be observed to be of decreasing importance for an increasing component of B perpendicular to the laser polarization \ensuremath{\epsilon}^. For laser intensities increasing beyond certain critical values, however, the fluorescence decreased and trapping seemed to become again important. For a quantitative explanation of the observed behavior we describe the system by generalized rate equations for the density matrix. We find that stimulated absorption and emission processes effectively inhibit the Larmor precession, thereby enforcing the trapping effect. Precession can only take place at sufficiently low light intensities.
This paper presents a theoretical analysis of a possible scheme to realize a strong population difference between the two ground state sub-levels F = 4, MF = 0, and F = 3, MF = 0 of caesium atom. Two laser-diode light beams, π polarized, are used to illuminate at right angle an atomic beam. The efficiency of the population difference build up is evaluated for two limiting cases according to the light spectral distribution : the monochromatic and broadband excitations. This analysis takes into account hyperfine and Zeeman structures of the energy levels. Numerical calculations show that the monochromatic excitation leads to steady state population difference close to the value obtained with a single pumping laser; however all the atoms can be brought in the upper level if the two laser lights are considered broadband and uncorrelated Guidelines are derived to obtain an efficient optically pumped caesium beam frequency standard.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1{D}_{1}D1​ line of the Rb\mathrm{Rb}Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with FFF and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s1\phantom{\rule{0.1em}{0ex}}\mathrm{s}1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s{10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.