Quantum treatment of two-stage sub-Doppler laser cooling of magnesium atoms

Abstract

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.

New approaches in deep laser cooling of magnesium atoms for quantum metrology

“…For short, we do not provide here the detailed formalism of our theory, which can be found in [3,7]. Let us just note that the standard quantum-mechanical approach for studying kinetics of atoms under electromagnetic fields based on the density matrix ρ is exploited.…”

“…However, strictly speaking, the semiclassical approximation is not valid in our case. Indeed, some of the basic requirements of the semiclassical approach can be violated even under the regular experimental conditions of laser cooling (e.g., see [3]). In particular, a typical width Δp of the momentum distribution f(p) can be of the order ħk.…”

“…This relatively young direction of designing the frequency standards has already demonstrated the values of fractional instability and inaccuracy on extremely low levels down to 10 -18 [2]. Magnesium atom has some advantages over the other candidates [3]. Unfortunately, deep laser cooling of magnesium atoms close to the recoil energy limit (several microkelvins) is the intricate problem in contrast to the other elements.…”

A scalable laser system at 461 nm for laser cooling and trapping of Sr atoms

“…The realization of laser sources led to the advent of ultracold atoms which in turn advanced various fields varying from high precision metrology [3][4][5][6] to quantum simulations [7]. For the new generation of frequency standards and atom interferometers, alkaline-earth atoms and alkaline-earth-like atoms such as Yb [8,9], Ca [10], Sr [11], Hg [12], Mg [13] and Cd [14] have been considered as interesting species.…”

Optical forces on neutral atoms in the presence of fluctuating laser fields: numerical analysis

“…Especially, the cold-trapped atoms are well-suited for an extensive range of applications such as atom localisation [5,6], atomic clocks [7][8][9], quantum sensors [10,11], and quantum gates [12]. Nowadays, the alkaline-Earth atoms (such as Mg, Ca, and Sr) are extensively used in laser cooling experiments due to their lack of hyperfine structure for the most abundant bosonic isotopes [13,14]. Indeed, this provides narrow electronic transitions which can be well-approximated to actual two-level systems [15,16].…”