1.5 μ m Lasers with Sub-10 mHz Linewidth

We report on two ultrastable lasers each stabilized to independent silicon Fabry-Pérot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of 4 ×10^-17 for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.