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European Frequency and Time Forum

Coherent population trapping ramsey resonance in slow rubidium beam

Igor M. Sokolov

Published Apr 1, 2016• 0 citations
Publisher

Abstract

We calculate the coherent population trapping (CPT) resonance in slow beam of rubidium 87 atoms caused by their interaction with laser bichromatic electromagnetic field in two separated spatial domains. We study influence of the finite width of the atomic beam, its angular divergence and residual beam velocity spread on the parameters of CPT-Ramsey resonance. We analyze properties of the CPT resonance depending on intensity of electromagnetic field, applied magnetic field strength and on width of the laser light beams.

DOI
10.1109/eftf.2016.7477762

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We calculate the coherent population trapping (CPT) resonance in slow beam of rubidium 87 atoms caused by their interaction with laser bichromatic electromagnetic field in two separated spatial domains. We study influence of the finite width of the atomic beam, its angular divergence and residual beam velocity spread on the parameters of CPT-Ramsey resonance. We analyze properties of the CPT resonance depending on intensity of electromagnetic field, applied magnetic field strength and on width of the laser light beams.
Formation of a coherent population trapping (CPT) resonance is studied in the interaction of a beam of atoms with two spatially separated domains of the dichromatic field. Various resonance excitation schemes are compared depending on the choice of operation transitions and type of the polarisation scheme. In the case of a single-velocity atomic beam, the dependence of the CPT resonance profile is studied as a function of principal parameters of the system: beam velocity, distance between optical fields, laser beam dimensions and intensities, and applied permanent magnetic field. Influence of the atomic beam angular divergence and residual beam velocity spread on the resonance quality parameter is estimated.
We examine experimentally and theoretically the Ramsey effects on the coherent population trapping (CPT) resonance in a paraffin-coated Rb vapor cell. The observed CPT spectrum in the Hanle configuration of the 5S 1/2(F = 2)−5P 1/2(F′ = 1) transition of 87Rb atoms consists of a narrow structure with a spectral width of 0.10 mG due to the wall-induced Ramsey effect and a broad structure with a spectral width of 23 mG due to the transit effect. Considering the velocity distribution of atoms and the number of wall-atom collisions, we numerically calculated the transmittance of the laser beam as a function of the longitudinal magnetic field. The experimental results of the CPT Ramsey interference were in good agreement with the theoretical results, and the dependences of the CPT Ramsey effects on the atom-laser interaction time were investigated in detail.
We calculated line-shapes of the coherent population trapping (CPT) for the open transition in 87Rb by solving time-dependent optical Bloch equations and averaging results for the total excited state populations over atomic trajectories and velocities, while taking into account incident angles to the laser beam. Comparison with experiment produces good agreement for the laser intensity dependence of the CPT line-widths when the laser transverse beam profile is Gaussian. This theoretical model was used to calculate the probe laser CPT in the case of spatially separated pump beam. The probe beam is placed inside the cylindrically-shaped pump beam. The calculations as well as measurements show narrowing of the Hanle resonance due to Ramsey effect.
This work is concerned with the line profiles, amplitudes and widths of the coherent population trapping (CPT) resonances due to low frequency Zeeman coherences, in the Hanle configuration, applied to 87Rb atoms in the vacuum cell. Detailed calculations of the fluorescence were done with two different transverse intensity profiles of the excitation laser tuned to the open Fg = 2 → Fe = 1 transition. Comparison with experiment produces good agreement for the laser intensity dependence of CPT line-widths in the wide range of the laser intensity, when the laser transverse beam profile is Gaussian. Results for both step-like and Gaussian profile of the laser beam show asymptotic 1/√d dependence (d is the laser beam diameter) of CPT line-widths, for large range of the laser intensity.
This work is devoted to a theoretical investigation of the Ramsey method of detection of the coherent population trapping resonance in cold atomic clouds taking into account collective effects caused by finite optical depth of the considered clouds. The interaction of atoms with pulsed laser radiation is described in the formalism of density matrix by means of Maxwell-Bloch set of equations. The Ramsey signal of coherent population trapping resonance was calculated for the radiation passed through the medium and analyzed for different length of the atomic cloud. Also the population of excited level was calculated in dependence on the two-photon detuning and coordinate along the main optical axis. The light shift of sidebands and appearance of additional harmonics were discovered.