Laser with an in-loop relative frequency stability of $1.0\times {10}^{-21}$ on 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 $1.9\times {10}^{-7}\text{Hz}/\sqrt{\text{Hz}}$ at 10 Hz for the 1064 nm laser; this value is limited by shot noise. The Allan standard deviation for relative frequency noise is $1.0\times {10}^{-21}$ 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.

Figure 1

(Color online) Laser frequency stabilization in two stages. Semicircled dots are symbols for photodetectors. “IMC” stands for the input mode-cleaner cavity, with suspended mirrors, in vacuum; “RC” stands for the short and rigid 30 cm cavity in vacuum; and “$\text{L}+$” stands for the common mode of the two 3 km cavities. The triangles represent correction filters. The IMC lock filter $\left(C_{\text{IMC}}\right)$ and the common mode filter $\left(C_{{\text{L}}_{+}}\right)$ are digital filters. The laser is prestabilized to the input mode-cleaner cavity; the second stage of stabilization uses the common mode of the interferometer as a reference.

Figure 2

(Color online) The solid line is the spectral density of the second stage of frequency stabilization error signal; the dotted line is the estimated out-of-loop shot noise stabilization limit; and the dashed line shows the specifications for the error signal of the second stage of laser frequency stabilization.

Figure 3

(Color online) Allan standard deviation, computed from the spectral density of the error signal of the second stage of frequency stabilization.

Figure 4

(Color online) Estimated fraction of laser frequency noise in the actual dark fringe channel.