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Optical pumping in rubidium-87 - Circular polarisation on the (Fg=2 - Fe=3) transition in the D2-line in the presence of a magnetic field

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 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.

DOI
10.6084/m9.figshare.3979227.v2

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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 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.
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.
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 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.