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Optical pumping in rubidium-87 - A mixture of sigma+ and sigma- circularly polarized light on the (Fg=1 - Fe=0) transition in the D2-line

Anders Kastberg, Fred Atoneche

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We present results of a method for calculating optical pumping rates in Rb-87, as described in Eur. J. Phys 38, 045703 (2017) We use a mixture of circularly polarized light (sigma+ and sigma-) on the (Fg=1 - Fe=0) transition to populate an angular momentum state in the Fg=1 hyperfine structure level of the ground state, with magnetic quantum number Mg=0 - that is a clock state. The method is shown to function well for the studied system. Explicit analytical equations for all level populations as functions of time, detuning, intensity, relative intensities of the polarization, and starting parameters are derived.

DOI
10.6084/m9.figshare.3750702.v3

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We present results of a method for calculating optical pumping rates in Rb-87, as described in Eur. J. Phys 38, 045703 (2017) We use a mixture of circularly polarized light (sigma+ and sigma-) on the (Fg=1 - Fe=0) transition to populate an angular momentum state in the Fg=1 hyperfine structure level of the ground state, with magnetic quantum number Mg=0 - that is a clock state. The method is shown to function well for the studied system. Explicit analytical equations for all level populations as functions of time, detuning, intensity, relative intensities of the polarization, and starting parameters are derived.
We present results of a method for calculating optical pumping rates in Rb-87, as described in Eur. J. Phys 38, 045703 (2017) We use light with an impure polarization (i.e. a mixture of sigma+, sigma- and pi light) to populate a stretched angular momentum state in the Fg=2 hyperfine structure level of the ground state. The method is shown to function well for the studied system. Absolute scale level populations as functions of time, detuning, intensity, relative intensity of polarizations, and starting parameters are derived.
We present results of a method for calculating optical pumping rates in Rb-87, as described in Eur. J. Phys 38, 045703 (2017) We use circularly polarized light to populate a stretched angular momentum state in the Fg=2 hyperfine structure level of the ground state. We include in the analysis an applied weak magnetic field. The method is shown to function well for the the studied system. Absolute scale level populations as functions of time, detuning, intensity, magnetic field and starting parameters are derived.
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.
We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.
We have studied the optical pumping of mixtures of Rb vapor and N2{\mathrm{N}}_{2}N2​ buffer gas by laser light tuned to the D1{D}_{1}D1​ transition having a spectral width of  500~500 500 MHz. The Rb densities are of the order of 1013{10}^{13}1013 cm${}^{\ensuremath{-}3}$, while the buffer-gas pressures range from 0.1 to 10 torr. As the frequency of the right-hand circularly polarized laser is varied across the D1{D}_{1}D1​ absorption profile, the electron spin polarization of the Rb is found to take on negative values for small negative values of pump detuning from the absorption profile center. This occurs for N2{\mathrm{N}}_{2}N2​ pressures below  1~1 1 torr; at 10 torr the electron spins consistently point in the same direction as the angular momentum of the pump light. The spin-reversal effect can be understood in terms of populations of the F=2F=2F=2 (85Rb^{85}\mathrm{Rb}85Rb) and F=1F=1F=1 (87Rb^{87}\mathrm{Rb}87Rb) states caused by small unpolarized fractions in the pump beam and its elimination in terms of pressure broadening caused by the N2{\mathrm{N}}_{2}N2​ buffer gas. We speculate that this effect could be used for fast Rb spin modulation.
Optical transition probabilities between the several magnetic sublevels of the Rb85{\mathrm{Rb}}^{85}Rb85 ground state via the first excited state are given separately for the two fine-structure components. Graphs of the populations of the states are presented as a function of the time the atoms are illuminated by circularly polarized resonance radiation.