# Nonlinear Spectroscopy of Alkali Atoms in Cold Medium of Astrophysical Relevance

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## Abstract

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## 1. Introduction

## 2. Formation of HF Absorption Multiplet for Partially Open Transitions

## 3. Experimental Setup and Spectroscopic Data

## 4. Cyclic Transitions Treatment: Modeling and Discussion

#### 4.1. Adiabatic Approach

#### 4.2. Strict Results

#### 4.3. Discussion of the Line–Shape Structure

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Transition strength ${\tilde{S}}_{{F}^{\u2033}{F}^{\prime}}$ (boxed) and branching $\Pi $ (circled) factors for the hyperfine components of D2-lines for (

**a**) cesium (transition ${6}^{2}{s}_{1/2}\to {6}^{2}{p}_{3/2}$) and (

**b**) sodium (transition ${3}^{2}{s}_{1/2}\to {3}^{2}{p}_{3/2}$) atoms. For cyclic (closed) transitions, the factor $\Pi $ = 1. The natural lifetime $\tau $ and saturation threshold ${\Omega}_{st}=1/(\tau \sqrt{2)}$ of the resonance states are $\tau $ = 30.5 ns and ${\Omega}_{st}$ = 3.7 MHz for Cs while $\tau $ = 16.4 ns and ${\Omega}_{st}$ = 6.9 MHz for Na, respectively.

**Figure 3.**Schematic diagram of the experimental setup for the production and excitation of a cold Cs atom beam.

**Figure 4.**Theoretical (solid curve, Equation (19)) and experimental [11] (dots) absorption profile of the D2-line of Cs upon an excitation of the closed ${F}^{\u2033}=4\to {F}^{\prime}=5$ transition in a cold sub-thermal Cs beam for laser power of 1.0 mW (the corresponding Rabi frequency $\Omega $ = 21.2 MHz). The dashed curve corresponds to the power broadening profile. The bar-dashed curve exhibits the natural broadening profile.

**Figure 5.**The same as in Figure 4 in the case of D2-line of sub-thermal Na atoms and the excitation of the closed ${F}^{\u2033}=2\to {F}^{\prime}=3$ transition with laser Rabi frequency $\Omega $ = 21.2 MHz.

**Figure 6.**(

**a**) schematic illustration of a three-level system having a cyclic transition $|4\u232a\to |2\u232a$ and a partially open transition $|3\u232a\to |2\u232a$ with the branching factor $\Pi $. The additional passive state $|1\u232a$ accumulates the population due to the spontaneous transition $|3\u232a\to |1\u232a$; (

**b**) the same scheme in the rotating wave approximation. The bare ground state $|2\u232a$ is selected as the position of zero energy (dashed horizontal line).

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**MDPI and ACS Style**

Efimov, D.K.; Bruvelis, M.; Bezuglov, N.N.; Dimitrijević, M.S.; Klyucharev, A.N.; Srećković, V.A.; Gnedin, Y.N.; Fuso, F. Nonlinear Spectroscopy of Alkali Atoms in Cold Medium of Astrophysical Relevance. *Atoms* **2017**, *5*, 50.
https://doi.org/10.3390/atoms5040050

**AMA Style**

Efimov DK, Bruvelis M, Bezuglov NN, Dimitrijević MS, Klyucharev AN, Srećković VA, Gnedin YN, Fuso F. Nonlinear Spectroscopy of Alkali Atoms in Cold Medium of Astrophysical Relevance. *Atoms*. 2017; 5(4):50.
https://doi.org/10.3390/atoms5040050

**Chicago/Turabian Style**

Efimov, Dmitry K., Martins Bruvelis, Nikolai N. Bezuglov, Milan S. Dimitrijević, Andrey N. Klyucharev, Vladimir A. Srećković, Yurij N. Gnedin, and Francesco Fuso. 2017. "Nonlinear Spectroscopy of Alkali Atoms in Cold Medium of Astrophysical Relevance" *Atoms* 5, no. 4: 50.
https://doi.org/10.3390/atoms5040050