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Quantum Electronics

Laser cooling of atoms at narrow optical transitions in fields with a polarisation gradient

R. Ya. Ilenkov, Прудников Олег Николаевич, A. V. Taǐchenachev, Valeriy I. Yudin

Published Jun 1, 2020• 0 citations
Publisher

Abstract

Abstract The efficiency of the polarisation mechanisms of laser cooling of atoms is analysed using narrow optical transitions for which the recoil energy is greater than or comparable to the natural line width. By the example of atoms with the J g = 1 → J e = 2 optical transition (J g and J e are the total angular momenta of the ground and excited states) in the resonant light fields of σ + – σ – and lin⊥lin configurations, the analysis of the minimum achievable energies of laser-cooled atoms is performed. It is shown that the polarisation mechanisms of laser cooling under conditions of a significant influence of recoil effects become less efficient and do not lead to average kinetic energies of an ensemble of atoms below the Doppler limit.

DOI
10.1070/qel17337

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Abstract The efficiency of the polarisation mechanisms of laser cooling of atoms is analysed using narrow optical transitions for which the recoil energy is greater than or comparable to the natural line width. By the example of atoms with the J g = 1 → J e = 2 optical transition (J g and J e are the total angular momenta of the ground and excited states) in the resonant light fields of σ + – σ – and lin⊥lin configurations, the analysis of the minimum achievable energies of laser-cooled atoms is performed. It is shown that the polarisation mechanisms of laser cooling under conditions of a significant influence of recoil effects become less efficient and do not lead to average kinetic energies of an ensemble of atoms below the Doppler limit.
Based on the numerical solution of the quantum kinetic equation for the atomic density matrix, which makes it possible to accurately take into account the recoil effects in the interaction of atoms with field photons, we have studied the limits of laser cooling of atoms using closed optical transitions characterised by different recoil parameters (the ratio of the recoil energy to the natural linewidth). It is shown that for optical transitions with an insufficiently small recoil parameter, the polarisation effects, which lead to the possibility of sub-Doppler laser cooling, lose their efficiency and do not ensure an attainment of the temperature below the Doppler limit. The analysis performed allows one to outline the boundaries of the sub-Doppler theory of laser cooling of atoms.
The laser cooling of atoms with a narrow-line optical transition, i.e., in regimes of quantum nature of laser-light interactions resulting in a significant recoil effect, is studied. It is demonstrated that a minimum laser-cooling temperature for two-level atoms in a standing wave reached for red detuning close to three recoil frequencies is vastly different from the theory used for a semiclassical description of Doppler cooling. A set of dimensionless parameters uniquely characterizing the time evolution and the steady state of different atoms with narrow-line optical transitions in the laser field is introduced. The results can be used for analysis of optimal conditions for laser cooling of atoms with narrow lines such as Ca, Sr, and Mg, which are of great interest for atomic clocks.
We study laser cooling of atoms with narrow-line optical transition, i.e. in regimes when quantum nature of laser-light interactions results significant effect on atom kinetics. We demonstrate the minimum of laser cooing temperature is reached for the light field detuning close to -3 recoil frequency, i.e. is much differ from standard Doppler cooling theory is used for semiclassical description of laser cooling. We define a set of dimensionless parameters that describe the steady state solution of cold atom distribution in laser light and cooling time. The results can be used for analysis an optimal conditions of laser cooling of atoms with narrow lines Ca, Sr and Mg are of interest for optical time standards.
We study the laser cooling of atoms with a narrow-line optical transition in monochromatic laser light, i.e. in regimes of quantum nature of laser-light interactions resulting in a significant recoil effect. It is demonstrated that a minimum laser cooling temperature for two-level atom in standing wave reached for red detuning close to 3 recoil frequency, greatly different from the theory used for a semiclassical description of Doppler cooling. A set of dimensionless parameters uniquely characterizing the time evolution and the steady state of different atoms with narrow-line optical transitions in the laser field is introduced. The results can be used for analysis of optimal conditions for laser cooling of atoms with narrow lines such as Ca, Sr, and Mg, which are of great interest for atomic clocks.
The theoretical description of the kinetics of neutral atoms in the polarized light fields with all the atomic levels, the coherence, the recoil effect is both important and challenging problem. The first step toward understanding mechanisms of interaction between atoms and light was called quasi-classical approach. [1,2] It lies in the fact that the equations for the density matrix can be reduced to the Fokker-Planck equation for the Wigner function in the phase space. But the semiclassical approximation is inapplicable for investigating the cooling of atoms at clock transitions, because the quasiclassical parameter (the recoil frequency) is not small (in comparison with the natural line width). Later quantum methods were developed [3], for example, the secular approach which describes cooling and localization of atoms in the optical potential. Secular approximation fails high vibrational levels and for atoms in high vibrational states.