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The frequency noise power spectral density of a free-running quantum cascade laser frequency comb is investigated. A plateau is observed at high frequencies, attributed to the quantum noise limit set by the Schawlow-Townes formula for the total laser power on all comb lines. In our experiment, a linewidth of 292 Hz is measured for a total power of 25 mW. This result proves that the four-wave mixing process, responsible for the comb operation, effectively correlates the quantum noise of the individual comb lines.

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