Control of a filter cavity with coherent control sidebands

For broadband quantum noise reduction of gravitational-wave detectors, frequency-dependent squeezed vacuum states realized using a filter cavity is a mature technique and will be implemented in Advanced LIGO and Advanced Virgo from the fourth observation run. To obtain the benefit of frequency-dependent squeezing, detuning and alignment of the filter cavity with respect to squeezed vacuum states must be controlled accurately. To this purpose, we suggest a new length and alignment control scheme, using coherent control sidebands which are already used to control the squeezing angle. Since both squeezed vacuum states and coherent control sidebands have the same mode matching conditions and almost the same frequency, detuning and alignment of the filter cavity can be controlled accurately with this scheme. In this paper, we show the principle of this scheme and its application to a gravitational-wave detector.