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Physical Review

Rubidium Transition Probabilities for Optical Pumping

W. Bruce Hawkins

Published Jun 5, 1969• 8 citations
Publisher

Abstract

Optical transition probabilities between the several magnetic sublevels of the ${\mathrm{Rb}}^{85}$ 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.

DOI
10.1103/physrev.182.39

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Physical Chemistry Chemical Physics•Jan 1, 2025•0 citations
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.
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.
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 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 analytical solutions for the populations of the D 1 transition line of 85 Rb atoms. The time evolution of the populations of the magnetic sublevels in the excited state at the weak intensity limit exhibits several kinds of homogeneous or inhomogeneous second-order differential equations. General solutions of the differential equations result in an analytical form of the population in each magnetic sublevel as a function of the elapsed time, laser intensity, and laser frequency detuning.
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.
Cs) atoms by applying circularly polarized light at an optimal frequency for electronic transitions from ground to excited states. To enhance control over sublevel populations following optical pumping, we incorporate a radiofrequency (RF) field. This integrated approach enables us to achieve a tailored distribution of atomic sublevel populations with high efficiency. Utilizing the Lindblad master equation, we provide a comprehensive framework for analyzing these dynamics, examining relaxation rates, repopulation processes, and the evolution of cesium Zeeman sublevels. Our findings underscore the effectiveness of the Lindblad master equation in accounting for external field effects and environmental interactions, significantly improving the accuracy and generalizability of optical pumping models. This method holds substantial promise for various applications in optical experiments, including magnetometry and quantum computing, paving the way for future advancements in these fields.