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.

Figure 1

Frequency relationship inside the filter cavity. Red dashed line is carrier, orange and blue lines are coherent control sidebands.

Figure 2

Phase of the filter cavity reflectivity. The horizontal axis is the sideband frequency normalized with respect to $\mathrm{\Delta }{\omega }_{\mathrm{fc},0}$. Black dashed lines are the sideband frequency of CCSB.

Figure 3

Filter cavity length signal normalized with respect to $a_{+}{a}_{-}$. The horizontal axis is the filter cavity detuning normalized with respect to $\mathrm{\Delta }{\omega }_{\mathrm{fc},0}$. Red solid and dashed lines are intracavity power of CCSB and carrier in the filter cavity normalized with respect to their maximum intracavity power, respectively. Blue and green lines are the filter cavity length signal (in-phase and quadrature). The filter cavity length signal (in-phase) becomes 0 when $\mathrm{\Delta }{\omega }_{\mathrm{fc}}=\mathrm{\Delta }{\omega }_{\mathrm{fc},0}$.

Figure 4

Filter cavity WFS signal as a function of the gouy phase normalized with $\sqrt{\frac{2}{\pi }}{a}_{+}{a}_{-}$. Red line is displacement signal with $\delta x={\mathrm{w}}_0$ and blue line is tilt signal with $\delta \theta ={\theta }_0$.

Figure 5

An example of experimental setup. Red solid line is the carrier and red dashed line is the squeezed vacuum states. Orange line is the coherent control field. Green line is the green pump field which is produced by the second harmonic generator (SHG) and injected into the OPO.

Figure 6

Coupling between CCFC loop and CC2 loop.

Figure 7

Quantum noise relative to coherent vacuum with $\delta L_{\mathrm{fc}}=1$ pm. Solid purple and black lines are frequency-dependent phase noise and total noise with this scheme. Dotted purple and black lines are frequency-dependent phase noise and total noise with conventional scheme. The solid lines and dotted lines are almost overlapping since the effect of frequency-dependent phase noise is small.

Figure 8

Quantum noise relative to coherent vacuum with $\delta L_{\mathrm{fc}}=3$ pm.

Figure 9

Coupling from input, end mirror misalignment of the filter cavity to the filter cavity length signal (a20) normalized with respect to $a_{+}{a}_{-}$. The coupling should be smaller than the filter cavity length signal $\sim 0.023$. Input, end mirror misalignment should be inside the ellipse corresponding to 0.023.