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Journal of Optical Technology

Calculation of the nonlinear interaction between a laser beam and alkali-metal atomic vapor in an ultrathin cell

G. Todorov, В. А. Полищук, A. Krasteva, Armen D. Sargsyan, S. Cartaleva, T. A. Vartanyan

Published Nov 1, 2016• 3 citations
Publisher

Abstract

We calculate the fluorescence and nonlinear absorption spectra of alkali-metal atomic vapor in ultrathin cells. We obtain closed-form equations for the nonlinear atomic polarization by applying perturbation theory to the intensity of linearly polarized laser light for arbitrary values of the total momenta of the resonant levels. The results of this calculation are consistent with experimental data obtained using an ultrathin cell filled with Cs133 vapor.

DOI
10.1364/jot.83.000659

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We calculate the fluorescence and nonlinear absorption spectra of alkali-metal atomic vapor in ultrathin cells. We obtain closed-form equations for the nonlinear atomic polarization by applying perturbation theory to the intensity of linearly polarized laser light for arbitrary values of the total momenta of the resonant levels. The results of this calculation are consistent with experimental data obtained using an ultrathin cell filled with Cs133 vapor.
The nonlinear absorption and fluorescence spectra of 133 Cs vapours confined to the extremely thin cell are computed in the framework of perturbation theory regarding to the intensity of the laser light illumination. The amplitude as well as the sign of the longitudinal alignment of the ground state is shown to be defined by the spontaneous decay of the upper level. The sign and the magnitude of the nonlinear absorption resonance on the closed optical transition are shown to be defined by this process as well.
Sub-Doppler resonances observed in miniature cells (V≪1cm3V \ll 1 cm^3V≪1cm3) with Rb or Cs atoms in the field of counterpropagating bichromatic laser beams are of interest for the creation of a miniature quantum frequency standard (QFS) of the optical range. However, a theory of these resonances that takes into full account the real structure of energy levels in an atom has not yet been constructed, which would make it possible to obtain explicit analytical expressions for the absorption coefficient of the medium. This paper addresses this gap using the density matrix formalism and the algebra of irreducible tensor operators. Namely, we obtained an analytical expression for the absorption coefficient of the probe beam in the presence of a more intense counterpropagating beam (pump-probe regime). Moreover, the calculations were carried out for arbitrary parameters of laser beam polarization, arbitrary angular momenta of optical dipole transitions in the atom and various relaxation processes. The constructed theory allows us to correctly take into account the simultaneous action of various nonlinear optical effects, in contrast to the simplified three-level model of the atom, and also to investigate the partial contribution of each of them to the overall observed resonant circuit. The analysis performed, in particular, made it possible to predict an increase in the amplitude of the sub-Doppler resonance when using counterpropagating light beams with opposite circular polarizations in relation to the configuration of counterpropagating beams with orthogonal linear polarizations, which is often used in practice.
The fluorescence and non-linear absorption spectra of Cs133 vapour in an extremely thin cell were calculated by using the perturbation theory with respect to the pumping field intensity. The problem of the atoms’ non-linear polarization was solved for arbitrary values of the total momenta of the resonance levels pumped by a linearly-polarised laser field. It was demonstrated that the spontaneous emission from the upper level affects the amplitude and sign of the lower level longitudinal alignment and results in a change of the amplitude and sign of the non-linear absorption resonance at the closed transition. The comparison of the numerical calculations with the experimental data for the D2 line of 133Cs shows a very good agreement.
Abstract High-contrast sub-Doppler resonances observed in alkali-metal atomic vapors in the field of counterpropagating bichromatic laser beams are perspective in quantum metrology for designing a miniature optical frequency standard. Until now, these nonlinear resonances have been investigated only experimentally or using numerical calculations. In our opinion, the development of a simplified theoretical model of the observed resonances, which would provide explicit compact analytic expressions describing the line shape of the resonance, would be extremely important for further evolution of the theory. In this study, we perform such theoretical analysis based on the three-level Λ scheme of the atom. We investigate two regimes, viz., the regime of a low-intensity standing wave with close intensities of counterpropagating beams (I1 ≈ I2) and the regime of a probe wave, in which one of the beams has a noticeably lower intensity than that of the oppositely propagating beam (I2 ≪ I1). The resulting analytic expressions make it possible to determine qualitative differences between these regimes and to separate explicitly the contributions from different nonlinear effects to the light field absorption, including the terms responsible for the formation of a high-contrast sub-Doppler peak. The expressions derived here are in qualitative agreement with experimental data obtained earlier.
Hot alkali metal vapors enclosed in submicron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at the nanoscale. Here, we propose an approach for calculating the eigenmodes of a thin vapor layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blueshift and deformation of the spectral line shapes of reflection, transmission, and absorption. We also demonstrate that the eigenmodes of the thin vapor layer can be calculated independently of the choice of optical boundary conditions. This greatly extends the applicability of the constructed theory for the development of miniature atomic sensors.
Hot alkali metal vapors enclosed in sub-micron spectroscopic cells provide an ideal system for fundamental studies of the atom-wall and atom-light interactions at nanoscale. Here, we propose a novel approach for calculating the eigenmodes of a thin-vapor-layer beyond the limitations of the first-order perturbation theory in optical density for the case of quenching of atomic polarization upon collisions of atoms with dielectric walls. We show that higher-order optical density corrections lead to a remarkable density-dependent blue shift and deformation of the spectral line shapes of reflection, transmission, and absorption. We also demonstrate that the eigenmodes of the thin-vapor-layer can be calculated independently of the choice of optical boundary conditions. This greatly extends the applicability of the constructed theory for the development of miniature atomic sensors.