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Note that the fluctuations of this force, arising from the spontaneous emission accompanying absorption, lead to a heating of the cloud, which limits the time scale of experiments. We come back to this issue in Sec. 7.
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The color coding and slashed lines denoting the regimes of stability come in fact from the analytical calculations detailed in Sec. 5, and not directly from simulations themselves (the computational cost is only linear with N, but simulations with N= 106 are still impractical). Therefore they correspond to stability with respect to infinitesimal perturbations. As such, they have been checked via simulation and seen to be correct several times, as illustrated in the examples in Figs. 9 10.
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