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arXiv:1812.09641 · Physical Review A

Dual-frequency sub-Doppler spectroscopy: Extended theoretical model and microcell-based experiments

Denis V. Brazhnikov, Michael Petersen, Grégoire Coget, Nicolas Passilly, Vincent N. Maurice, Christophe Gorecki, Rodolphe Boudot

Published Jun 17, 2019• 36 citations
arXivHTMLPDF

Abstract

Sub-Doppler spectroscopy in alkali-metal vapor cells using two counterpropagating dual-frequency laser beams allows the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances. Previously, a qualitative theory based on a simplified \ensuremath{\Lambda}-scheme model has been reported to explain underlying physics of this phenomenon. In this paper, an extended theoretical model of dual-frequency sub-Doppler spectroscopy (DFSDS) for the Cs ${D}_{1}$ line is reported. Taking into account the real atomic energy structure, main relaxation processes, and various nonlinear effects, this model describes quantitatively the respective contributions of involved physical processes and predicts main properties (height and linewidth) of the sub-Doppler resonances. Experimental tests are performed with a Cs vapor microfabricated cell and results are found to be in correct agreement with theoretical predictions. Spatial oscillations of the sub-Doppler resonance amplitude with translation of the reflection mirror are highlighted. A beat note between two laser systems, including one stabilized with DFSDS on a Cs vapor microcell, yields a fractional frequency stability of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ until 10-s averaging time. These results demonstrate that DFSDS could be an interesting approach for the development of a high-performance microcell-based optical frequency reference, with applications in various compact quantum devices.

DOI
10.1103/physreva.99.062508

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Journal of Experimental and Theoretical Physics•Dec 1, 2021•7 citations
Sub-Doppler spectroscopy in alkali-metal vapor cells using two counterpropagating dual-frequency laser beams allows the detection of high-contrast sign-reversed natural-linewidth sub-Doppler resonances. Previously, a qualitative theory based on a simplified \ensuremath{\Lambda}-scheme model has been reported to explain underlying physics of this phenomenon. In this paper, an extended theoretical model of dual-frequency sub-Doppler spectroscopy (DFSDS) for the Cs D1{D}_{1}D1​ line is reported. Taking into account the real atomic energy structure, main relaxation processes, and various nonlinear effects, this model describes quantitatively the respective contributions of involved physical processes and predicts main properties (height and linewidth) of the sub-Doppler resonances. Experimental tests are performed with a Cs vapor microfabricated cell and results are found to be in correct agreement with theoretical predictions. Spatial oscillations of the sub-Doppler resonance amplitude with translation of the reflection mirror are highlighted. A beat note between two laser systems, including one stabilized with DFSDS on a Cs vapor microcell, yields a fractional frequency stability of 2\ifmmode×\else\texttimes\fi10\ensuremath−12\ensuremathτ\ensuremath−1/22\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}2\ifmmode×\else\texttimes\fi10\ensuremath−12\ensuremathτ\ensuremath−1/2 until 10-s averaging time. These results demonstrate that DFSDS could be an interesting approach for the development of a high-performance microcell-based optical frequency reference, with applications in various compact quantum devices.
The combination of atomic spectroscopy, integrated photonics, and microelectromechanical systems leads the way to the demonstration of microcell-based optical atomic clocks. Here, we report the short-term stability budget of table-top Cs microcell-stabilized lasers based on dual-frequency sub-Doppler spectroscopy (DFSDS). The dependence of the sub-Doppler resonance properties on key experimental parameters is studied. The detection noise budget and absolute phase noise measurements are in good agreement with the measured short-term frequency stability of the laser beatnote, at the level of 1.1 × 10 − 12 τ − 1 / 2 until 100 s, currently limited by the intermodulation effect from a distributed-feedback laser setup. The fractional frequency stability of the laser beatnote at 1 s is about 100 times greater than that of commercial microwave chip-scale atomic clocks and validates interest in the DFSDS approach for the development of high-performance microcell-based optical standards.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1{D}_{1}D1​ line of the Rb\mathrm{Rb}Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with FFF and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s1\phantom{\rule{0.1em}{0ex}}\mathrm{s}1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s{10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.
We report on Doppler-free laser spectroscopy in a Cs vapor cell using a dual-frequency laser system tuned on the Cs D1 line. Using counter-propagating beams with crossed linear polarizations, an original sign reversal of the usual saturated absorption dip and large increase in Doppler-free atomic absorption is observed. This phenomenon is explained by coherent population trapping (CPT) effects. The impact of laser intensity and light polarization on absorption profiles is reported in both single-frequency and dual-frequency regimes. In the latter, frequency stabilization of two diode lasers was performed, yielding a beat note fractional frequency stability at the level of 3×10−12 at 1 s averaging time. These performances are about an order of magnitude better than those obtained using a conventional single-frequency saturated absorption scheme.
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.
Recently, the new bright feature of Doppler-free resonance in a cesium vapor cell under the twofrequency counterpropagating light waves has been observed [1] (see Fig.1). It consists in observation of a natural-linewidth nonlinear resonance with very high contrast. In spite of this effect is becoming very useful tool for laser frequency stabilization in CPT atom clocks [2, 3], it has not been understood and studied well enough. Here we focus on the detailed experimental as well as theoretical study of the new effect. Three physical reasons have been revealed that can result in observation of enhanced absorption at the center of the resonance. Moreover, simultaneous and constructive action of thesereasons can greatly increase amplitude of the nonlinear resonance, which can be two times bigger than a wide Doppler background. Theory is based on a well-known -scheme of atomic energy levels. The scheme has provided us with very clear physical interpretation of the effect. The real structure of atomic energy levels with taking into account all magnetic sublevels has been also considered.
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.