The problem of deep laser cooling of 24 Mg atoms is theoretically studied. We propose two-stage sub-Doppler cooling strategy using electro-dipole transition 3 3 P2→3 3 D3 (λ = 383.9 nm). The first stage implies exploiting magneto-optical trap with σ + and σ − light beams, while the second one uses a lin⊥lin molasses. We focus on achieving large number of ultracold atoms (T ef f <10 µK) in a cold atomic cloud. The calculations have been done out of many widely used approximations and based on quantum treatment with taking full account of recoil effect. Steady-state average kinetic energies and linear momentum distributions of cold atoms are analyzed for various light field intensities and frequency detunings. The results of conducted quantum analysis have revealed noticeable differences from results of semiclassical approach based on the Fokker-Planck equation. At certain conditions the second cooling stage can provide sufficiently lower kinetic energies of atomic cloud as well as increased fraction of ultracold atoms than the first one. We hope that the obtained results can assist overcoming current experimental problems in deep cooling of 24 Mg atoms by means of laser fields. Cold magnesium atoms, being cooled in large number down to several µK, have certain interest, for example, in quantum metrology.

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Two approaches for solving the long-standing problem of deep laser cooling of neutral magnesium atoms are proposed. The first one uses optical molasses with orthogonal linear polarizations of light waves. The second approach involves a 'nonstandard' magneto-optical trap (NMOT) composed of light waves with elliptical polarizations (in general). Both the widely used semiclassical approach based on the Fokker-Planck equation and quantum treatment fully taking into account the recoil effect are employed for theoretical analysis. The results show the possibility of obtaining temperatures lower than 100 µK simultaneously with a large number of cold atoms ~10 6 ÷ 10 7 . A new velocity-selective cooling technique allowing one to reach the microkelvin temperature range is also proposed. This technique may have some advantages over, for instance, the shallow-dipole-trap technique utilized by other authors. In the case of magnesium atoms this new technique may be used for obtaining a large number of ultracold atoms (T ~ 1 µK, N > 10 5 ). Such a large number of ultracold atoms is crucial issue for metrological and many other applications of cold atoms.

We present the theoretical analysis of sub-Doppler laser cooling of 24 Mg atoms using dipole transition 3 3 P 2 →3 3 D 3 under two counterpropagating light waves with opposite circular polarizations (one-dimensional σ + σconfiguration). For numerical calculations the standard semi-classical approach based on the Fokker-Planck equation for linear momentum distribution of atoms is exploited. The distributions are gained beyond the limits of slow atoms approximation and for an arbitrary light field intensity. The absence of these limits allows us to determine the optimal parameters of the light field to maximize a fraction of ultracold atoms (T ~ 10 μK) in a whole atomic cloud. In particular, under certain conditions the fraction can reach a value of 50%. Solution of the existing problems in deep laser cooling of magnesium atoms has obvious prospects for atomic optics and quantum metrology: for instance, in designing newgeneration optical frequency and time standards based on cold atoms in optical lattices.

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