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The collective atomic recoil lasing is studied for an ultra-cold andcollisionless atomic gas in a partially coherent pump with a colored noise.Compared to white noise, correlations in colored noise are found to be able togreatly enhance or suppress the growth rate, above or below a criticaldetuning. Effects on cooperative scattering of light for noise correlationtime, noise intensity and pump-probe detuning are discussed. This result isconsistent with our simulation and linear analysis about the evolutionequations in the regions of instability.

Cooperative atomic scattering of light from a laser with a colored noise spectrum