Doppler cooling on a narrow transition is limited by the noise of single scattering events. It shows novel features, which are in sharp contrast with cooling on a broad transition, such as a non-Gaussian momentum distribution, and divergence of its mean square value close to the resonance. We have observed those features using 1D cooling on an intercombination transition in strontium, and compared the measurements with theoretical predictions and Monte Carlo simulations. We also find that for a very narrow transition, cooling can be improved using a dipole trap, where the clock shift is canceled.
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