Simulation of atomic motion by random shift of transition frequencies in the method of coupled dipoles

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Abstract

We study the influence of atomic motion on the optical properties of atomic ensembles cooled in special laser traps. We analyze the possibility to simulate the continuous displacement of atoms within the framework of motionless coupled dipoles method, in which slow motion is modeled, firstly, by averaging over their random spatial distribution, and, secondly, by introducing a random shift of their frequencies, simulating Doppler effects. A direct comparison of the results obtained for moving atoms with the model ones revealed a very limited range of applicability of the latter.

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About the authors

A. P. Ammosov

Peter the Great Saint Petersburg Polytechnic University

Email: sokolov_im@spbstu.ru
Russian Federation, Saint Petersburg

G. V. Voloshin

Peter the Great Saint Petersburg Polytechnic University

Email: sokolov_im@spbstu.ru
Russian Federation, Saint Petersburg

Ya. A. Fofanov

Institute for Analytical Instrumentation of the Russian Academy of Sciences

Email: sokolov_im@spbstu.ru
Russian Federation, Saint Petersburg

I. M. Sokolov

Peter the Great Saint Petersburg Polytechnic University; Institute for Analytical Instrumentation of the Russian Academy of Sciences

Author for correspondence.
Email: sokolov_im@spbstu.ru
Russian Federation, Saint Petersburg; Saint Petersburg

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Supplementary files

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2. Fig. 1. Comparison of the excitation spectra of atoms in the ensemble obtained by modelling the motion by Doppler shifts (curves 1 and 2) and by explicitly taking into account the displacement of atoms with time (curves 3 and 4), n = 10-1k30. Curves 1 and 3 correspond to k0v0 = 0.1γ, curves 2 and 4 to k0v0 = 0.5γ

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3. Fig. 2. Dynamics of the instantaneous fluorescence delay time for an ensemble of atoms at k0v0 = 0.05 calculated by modelling the motion by Doppler shifts (1) and accounting for the displacement of atoms with time (2). For comparison, curve 3 is shown corresponding to stationary atoms

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4. Fig. 3. Comparison of the diffusion film time τd calculated by the coupled oscillator method taking into account the continuous displacement of atoms (1) and by the same method but modelling the motions by frequency shifts (2)

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5. Fig. 4. Dependence of the averaged transmittance of the atomic ensemble Tr on its thickness k0L at different temperatures. For convenience, the transmittance multiplied by the ensemble thickness k0LTr is given. Curves 1, 3, 5 are calculated taking into account the continuous displacement of atoms, 2, 4, 6 - modelling of motion by random shifts of transition frequencies of fixed atoms. The pairs of curves 1 and 2, 3 and 4, 5 and 6 are obtained for k0v0 = 0.1γ, k0v0 = 0.025γ and k0v0 = 0.05γ, respectively

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