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Quantum Electronics

Narrowing of the coherent population trapping resonance under zone pumping in cells with different characteristics of the wall coating

Georgy A. Kazakov, A N Litvinov, Boris G. Matisov

Published Feb 28, 2012• 7 citations
Publisher

Abstract

It is shown that when coherent population trapping (CPT) resonance is excited by a narrow laser beam, the presence of elastic collisions with the cell wall significantly affects the line shape of the CPT-resonance. We have constructed a theoretical model, which is based on averaging over the random Ramsey sequences of the atom dwell time in the beam and dark zones and takes into account the probability of elastic bounce of an atom from the wall.

DOI
10.1070/qe2012v042n02abeh014744

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It is shown that when coherent population trapping (CPT) resonance is excited by a narrow laser beam, the presence of elastic collisions with the cell wall significantly affects the line shape of the CPT-resonance. We have constructed a theoretical model, which is based on averaging over the random Ramsey sequences of the atom dwell time in the beam and dark zones and takes into account the probability of elastic bounce of an atom from the wall.
We studied theoretically a coherent population trapping resonance formation in cylindrical cell without buffer gas irradiated by a narrow laser beam. We take into account non-zero probabilities of elastic ("specular") and inelastic ("sticking") collision between the atom and the cell wall. We have developed a theoretical model based on averaging over the random Ramsey pulse sequences of times that atom spent in and out of the beam. It is shown that the shape of coherent population trapping resonance line depends on the probability of elastic collision.
We study the peculiarities of the coherent population trapping (CPT) dark resonance in atomic vapor confined in a finite-size cell. Taking into account the scattering of atoms on anti-relaxation coating of the walls, we analyze the line shape of the CPT resonance in 133 C s depending on various parameters, such as the width of laser radiation spectrum, the type of pumping, and the magnitude of static magnetic field for both lin || lin and l i n ⊥ l i n polarization schemes. We show that for different parameters, the dependence of the line shape on the size of a cell is different, i.e., different factors affect the CPT resonance nonadditively. Thus, in the case when CPT resonance is excited by a narrowband laser, the shape of the resonance weakly depends on the size of a cell due to the laser-induced narrowing effect. We also show that the distortion of the line shape of the CPT resonance caused by nonresonant hyperfine sublevels of atomic excited states is modified with the size of a cell. Our calculation reveals the important role of accounting for the hyperfine and Zeeman structure of atomic levels. We have shown that the contrast of the CPT resonance differs about 5 times from the prediction of the simple three-level Λ model. The obtained results can be used for the optimization of the quantum frequency standards based on the CPT effect. In the final part of the paper, on the basis of the shot noise approximation we estimate the short-term stability of such standards.
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.
The shape of the coherent population trapping resonance in optically thin cells with antirelaxation coating of the walls has been determined by solving the quantum kinetic equation for the single-atom density matrix. It has been found that motion and collisions with walls in the case of nondegenerate ground and excited states result in a significant change in the shape of the spectrum, in the appearance of a comb of additional resonances, and in shifts of the main resonance of coherent population trapping, which nonmonotonically depend on the size of the cell.