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We develop a nonlinear theory of propagation of a monochromatic light wave in a gas of two-level atoms under the condition of inhomogeneous Doppler lineshape broadening, while considering a self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation using a single atom density matrix formalism. Our approach shows a significant deformation of the Doppler resonant lineshape (shift, asymmetry), which depends on the atomic density. These effects are a consequence of only the free motion of atoms in a gas and is not associated with interatomic interaction. In particular, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole–dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the effect of the interatomic interaction by three orders of magnitude. The found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.

We consider the kinetics of atoms in nonuniform spatially polarised light fields resonant to the quadrupole optical transition with F g → F e = F g + 2 (F g,e is the total angular momentum in the ground and excited states). The lowest possible temperatures of laser cooling of atoms are analysed numerically and the results are compared with the data obtained for sub-Doppler cooling using light waves resonant to electric dipole optical transitions.

The interatomic dipole–dipole interaction is commonly thought to be the main physical reason for spectroscopic effects, which are nonlinear in atomic density. However, we have found that the free motion of atoms can lead to other effects that are nonlinear in atomic density n , using a previously unknown self-consistent solution of the Maxwell–Bloch equations in the mean-field approximation for a gas of two-level atoms with an optical transition at unperturbed frequency ω 0 . These effects distort the Doppler lineshape (shift, asymmetry, broadening), but are not associated with an atom–atom interaction. In particular, in the case of n k 0 − 3 < 1 (where k 0 = ω 0 / c ) and significant Doppler broadening (with respect to collisional broadening), atomic-motion-induced nonlinear effects significantly exceed the well-known influence of the dipole–dipole interatomic interaction (e.g., Lorentz–Lorenz shift) by more than one order of magnitude. Moreover, under some conditions, a frequency interval appears in which a non-trivial self-consistent solution of the Maxwell–Bloch equations is absent due to atomic motion effects. Thus, the existing physical picture of spectroscopic effects that are nonlinear in atomic density in a gas medium should be substantially revised.

The results of theoretical and experimental studies aimed at the creation of matter wave interferometers with Mg atoms are presented. Atom-optical interferometers based on the Ramsey-Bordé scheme are of great interest for the development of optical frequency standards. Ultracold Mg atoms are promising for the development of an optical frequency standard with relative uncertainty and long-term frequency instability at a level of 10−17 − 10−18. A long-term frequency stability of 3·10−15 is obtained at an averaging time τ = 103 s while stabilizing the frequency of a ‘clock’ laser at 457 nm (1 S 0 → 3 P 1 transition) to narrow Ramsey-Bordé resonances of Mg atoms cooled and localized in a magneto-optical trap. The measured frequency stability is determined by the stability of the measurement system based on an optical frequency comb stabilized to the optical frequency of a Yb:YAG/I2 standard. We also present the results of theoretical studies aimed at the use of Mg atom interferometers based on Bragg diffraction for quantum sensing.