Laser with an in-loop relative frequency stability of1.0×10−21on a 100-ms time scale for gravitational-wave detection

We report on the stabilization of the laser frequency for the Virgo gravitational-wave detector. We have obtained a frequency noise level, measured in loop, of 1.9×10−7 Hz/sqrt(Hz) at 10 Hz for the 1064 nm laser; this value is limited by shot noise. The Allan standard deviation for relative frequency noise is 1.0×10−21 on a 100-ms time scale. The spectral density of the laser frequency noise is negligible in the channel where gravitational waves ought to appear and meets the specifications for the target spectral resolution of the Virgo interferometer in the 10 Hz-10 kHz detection bandwidth.