Demonstration of length control for a filter cavity with coherent control sidebands

For broadband quantum noise reduction of gravitational-wave detectors, a frequency-dependent squeezed vacuum field realized using a filter cavity is the most promising technique and will be implemented in Advanced LIGO and Advanced Virgo in the fourth observing run. To obtain the benefit of frequency-dependent squeezing, the length and alignment of the filter cavity with respect to the squeezed vacuum field must be accurately controlled. To this purpose, a new length and alignment control scheme for a filter cavity, using coherent control sidebands, was suggested [Phys. Rev. D 102, 042003 (2020)]. The coherent control sidebands are already used to control the squeezing angle in squeezed vacuum sources for gravitational-wave detectors. As both the squeezed vacuum field and coherent control sidebands have the same mode-matching conditions and almost the same frequency, the length and alignment of the filter cavity with respect to the squeezed vacuum field can be accurately controlled with this scheme. In this paper, we experimentally demonstrate the new control scheme for a filter cavity with coherent control sidebands. In addition to the conventional filter cavity control with the green field, we succeed in controlling the length of a 300-m filter cavity with coherent control sidebands and reduce the filter cavity length noise (rms) from 6.8 to 2.1 pm.