Experiments on open transitions of the D 1 line of alkali metals (Cs and Rb isotopes) reveal the dual structure of saturated absorption resonance in the signal of a high-intensity optical wave in the presence of a low-intensity counterpropagating wave. Theoretical analysis shows that the observed shape of the resonance is associated with the openness of the atomic transition as well as with the Doppler effect for atoms in a gas. The results are of general physical significance for nonlinear spectroscopy and can also find application in metrology (frequency and time standards on open transitions).
Experiments on open transitions of the D 1 line of alkali metals (Cs and Rb isotopes) reveal the dual structure of saturated absorption resonance in the signal of a high-intensity optical wave in the presence of a low-intensity counterpropagating wave. Theoretical analysis shows that the observed shape of the resonance is associated with the openness of the atomic transition as well as with the Doppler effect for atoms in a gas. The results are of general physical significance for nonlinear spectroscopy and can also find application in metrology (frequency and time standards on open transitions).
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.
The effect of a double structure of saturated absorption resonance in the field of counterpropagating light waves interacting with an atomic gas is studied. The experimental observation of this effect was first reported in 2011 in a work by our colleagues at the P.N. Lebedev Physical Institute of the Russian Academy of Sciences (Laboratory of Frequency Standards). The essence of the effect lies in the fact that, on exciting an open dipole transition, another, narrower, resonance of an opposite sign can be observed at the center of the ordinary saturated absorption resonance. A theoretical analysis of this effect has also been performed in this work in terms of a simple spectroscopic model of an atom with two nondegenerate energy levels without taking into account higher spatial harmonics of atomic polarization and polarizations of light waves (scalar model). The present work is devoted to the development of a theory of the formation of a central narrow resonance for the example of a real F g = 1 → F e = 1 atomic transition and to the study of its main characteristics (amplitude, width, contrast, and amplitude-to-width ratio). In addition, the theoretical results obtained without taking into account the influence of higher spatial harmonics and with inclusion of the influence of first higher harmonics are compared. This comparison shows that their influence on the parameters of the new nonlinear resonance is strong even in moderately intense light fields (R ~ γ, where R is the Rabi frequency). The results of this study can be of interest for quantum metrology, as well as for many experiments in which the laser-radiation frequency is stabilized by the saturated absorption resonance on open dipole transitions in atoms and molecules.
The resonance of saturated absorption in counterpropagating light fields is experimentally and theoretically studied. We focus on a case of parallel and linearly polarized waves, driving an open dipole transition in rubidium vapor. A new Doppler-free resonance within the saturated-absorption dip is revealed. The phenomenon can be gained only in absorption of strong wave in presence of weak one. The effect can not be explained basing on the previously known reasons. The results obtained can be found useful in metrology for the frequency and time standards.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
The peculiarities of intra-Doppler structures that are observed in the atomic absorption spectrum of alkali metals with the help of two independent lasers have been studied. These structures accompany ultranarrow coherent resonances of electromagnetically induced transparency and absorption. With the D 2 line of rubidium taken as an example, it is shown that, in the scheme of unidirectional waves, the maximum number of satellite resonances caused by optical pumping selective with respect to the atomic velocity is equal to seven, while only six resonances are observed in the traditional scheme of saturated absorption with counterpropagating waves of the same frequency. The spectral position of the resonances and their polarity depend on the frequency of the saturating radiation, while their number and relative amplitude depend also on the experimental geometry. These features are of general character and should show themselves in the absorption spectrum on the D 2 lines of all alkali metals. An explanation of these features is given. The calculated spectral separations between the resonances are compared to the experimental ones, and their possible application is discussed.
Sub-Doppler resonances in caesium vapours are studied in a laser field produced by counterpropagating two-frequency light beams with mutually orthogonal linear polarisations. The beams are in resonance with optical transitions in the D1 line, the frequency difference of the field spectral components being equal to the hyperfine ground-state splitting in the Cs atom (≈9.2 GHz). It has already been shown that in this configuration, the hypercontrast effect can be observed for sub-Doppler resonances, which makes this configuration promising for the employment in newgeneration miniature optical frequency standards. In the present work, two different two-frequency configurations are compared with each other and with the single-frequency configuration widely used in practice for observing saturated absorption resonances. The parameters of nonlinear resonances are measured at various temperatures of caesium vapours and at different optical field intensities. The results of the investigations performed make it possible to find an optimal two-frequency scheme for exciting nonlinear resonances and to estimate a potential of the scheme for its applications in quantum metrology.