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Quantum Electronics and Laser Science Conference

Laser cooling and the recoil limit

S. L. Rolston, Paul D. Lett, William D. Phillips

Published Apr 24, 1989• 0 citations
OpenAlex

Abstract

The usual case in laser cooling is that the atomic linewidth ħγ is much greater than the recoil energy ER = ħ2k2/2 m. Considering the recent demonstration of laser cooling to kBT <<ħγ,1 It seems reasonable to reconsider laser cooling where ERħγ. In this case the Doppler shift ħk2/m of a recoil velocity is large compared to the linewidth and an analytic treatment is difficult. We have developed a Monte Carlo simulation of 3-D laser cooling (optical molasses) which applies to any value of ħγ/ER.

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The usual case in laser cooling is that the atomic linewidth ħγ is much greater than the recoil energy ER = ħ2k2/2 m. Considering the recent demonstration of laser cooling to kBT <<ħγ,1 It seems reasonable to reconsider laser cooling where ERħγ. In this case the Doppler shift ħk2/m of a recoil velocity is large compared to the linewidth and an analytic treatment is difficult. We have developed a Monte Carlo simulation of 3-D laser cooling (optical molasses) which applies to any value of ħγ/ER.
We present a quantum theory of one-dimensional laser cooling of free atoms using a transition with a J = 0 ground state and a J = 1 excited state. This treatment is valid both for broad lines (recoil energy small compared with the energy width ℏ Γ of the excited level) and for narrow lines. For broad lines we recover the well-known cooling limit for a two-level transition (∼ℏΓ/2), whereas for a narrow line the cooling limit is found to be of the order of the recoil energy. The stationary momentum distribution is obtained for both cases and is found to be close to the one obtained by Monte Carlo simulations.
Laser cooling on transitions with a linewidth Γ much narrower than the recoil shift ℏk2/m is studied numerically according to a full quantum-mechanical treatment of the photon recoil. We propose and investigate a broadband spectral configuration that has the purposes of (1) shortening the long cooling time characteristic for monochromatic laser cooling on a slow transition and (2) reducing the kinetic energy of the stationary momentum distributions considerably below the one-photon recoil energy (ℏk)2/2m. The energies of the computed stationary distributions are limited only by the energy uncertainty of the narrow transition ℏΓ ≪ (ℏk)2/2m. Applications to laser cooling of alkaline earths on the narrow intercombination lines are discussed.
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.
Abstract The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio between the natural linewidth and the recoil energy and tends to E R as tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio and contains the semiclassical theory of laser cooling as the limiting case in which .