Audio-Band Frequency-Dependent Squeezing for Gravitational-Wave Detectors

Quantum vacuum fluctuations impose strict limits on precision displacement measurements, those of interferometric gravitational-wave detectors among them. Introducing squeezed states into an interferometer’s readout port can improve the sensitivity of the instrument, leading to richer astrophysical observations. However, optomechanical interactions dictate that the vacuum’s squeezed quadrature must rotate by 90° around 50 Hz. Here we use a 2-m-long, high-finesse optical resonator to produce frequency-dependent rotation around 1.2 kHz. This demonstration of audio-band frequency-dependent squeezing uses technology and methods that are scalable to the required rotation frequency and validates previously developed theoretical models, heralding application of the technique in future gravitational-wave detectors.

Figure 1

Audio-band frequency-dependent squeezed vacuum source. Frequency-independent squeezed vacuum is produced using a dually resonant subthreshold OPO operated in a traveling-wave configuration. The OPO is pumped with light provided by a second harmonic generator (SHG). The generated squeezed state is subsequently injected into a dichroic ($1064/532\mathrm{nm}$) filter cavity along path (A) where it undergoes frequency-dependent quadrature rotation. A Faraday isolator redirects the returning squeezed field along path (B) towards a homodyne readout system where frequency-dependent squeezing is measured.

Figure 2

Demonstration of frequency-dependent squeezing. Measured noise relative to that due to the naturally occurring vacuum state (shot noise) as a function of sideband frequency and readout quadrature $\varphi$. The difference between the experimental filter cavity detuning (offset from resonance) and the desired value of 1248 Hz is denoted by $\mathrm{\Delta }\gamma$. Dashed curves represent the output of the model described in [18] using the parameters given in the legend and Table 1. The solid black curve provides an estimate of the overall improvement achievable if this frequency-dependent squeezed vacuum source were applied to the appropriate interferometer. Ellipses illustrate the modeled squeezing magnitude and angle (Wigner function) at the frequency at which they are located. The measured noise is given by the projection of the ellipse onto the appropriately colored readout vector.