Realistic filter cavities for advanced gravitational wave detectors

The ongoing global effort to detect gravitational waves continues to push the limits of precision measurement while aiming to provide a new tool for understanding both astrophysics and fundamental physics. Squeezed states of light offer a proven means of increasing the sensitivity of gravitational wave detectors, potentially increasing the rate at which astrophysical sources are detected by more than 1 order of magnitude. Since radiation pressure noise plays an important role in advanced detectors, frequency-dependent squeezing will be required. In this paper we propose a practical approach to producing frequency-dependent squeezing for Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and similar interferometric gravitational wave detectors. This work focuses on “realistic filter cavities” in the sense that optical losses in the filter cavity and squeezed light source consistent with current technology are considered. The filter cavity solution proposed for Advanced LIGO is “practical” in that it considers the nonquantum noise and readout scheme of the interferometer and a potential implementation geometry in the Advanced LIGO vacuum envelope.

Figure 1

The sensitivity of an Advanced LIGO-like detector, our baseline (see Table  for parameters), is limited at most frequencies by quantum noise, though at low frequencies thermal noise also contributes significantly (all other fundamental noise sources are less significant). In terms of quantum noise, 6 dB of squeezing is equivalent to a 4-fold increase in light power circulating in the interferometer, though always somewhat worse at low frequencies due to the degradation of the squeezed vacuum state by optical losses and technical noises [28]. All of the curves in this paper assume 5% injection loss (e.g., from the squeezed vacuum source to the interferometer) and 10% readout loss (e.g., from the interferometer to the readout, including the photodetector quantum efficiency).

Figure 2

A broadband squeezed vacuum state of light with a frequency-dependent squeezing angle can be produced with the help of a filter cavity. Shown here is a simplified interferometer with a linear “input filter cavity” [12].

Figure 3

Frequency-dependent squeezing decreases both shot noise and radiation pressure noise, reducing quantum noise at all frequencies (blue curve). A lossy filter cavity has degraded performance in the radiation pressure dominated region relative to an ideal lossless filter cavity (purple curve; see Table  for parameters). The lossy filter shown here, with $1\mathrm{ppm}/\mathrm{m}$ round-trip loss, represents a significant advantage over frequency-independent squeezing in that it prevents an increase in radiation pressure noise (green dashed curve; see Fig. 1). Furthermore, since thermal noise is significant in the region where radiation pressure noise acts, there is little to be gained by making a lower loss filter cavity in the context of a near-term upgrade to Advanced LIGO.

Figure 4

Measured round-trip loss per length from the literature [29, 30, 31, 32, 33]. Losses grow with beam size on the optics, so a confocal geometry is optimal for minimizing losses and is a good choice for a filter cavity [34]. To remove any dependence on the choice of cavity geometry in the experiments presented here, the beam sizes on the optics are used to scale the cavity length to that of an equivalent confocal cavity. A rough fit to these data is included to guide the eye, and our target value of $1\mathrm{ppm}/\mathrm{m}$ in a 16 m cavity is marked.

Figure 5

Various geometries considered for implementing a filter cavity. Factors considered in choosing among these geometries were cavity length per mirror, potential for scatter into a countercirculating mode, mode quality degradation due to large angle reflection from curved optics, and the ease of separating incident and reflected fields. While a linear cavity (option A) requires an optical isolator to separate input and output fields, it has the best length per mirror, no counter circulating mode, and good mode quality. A polarization based optical isolator will introduce about 1% loss in the squeezed field injection, but this is outside of the filter cavity and modest compared to the 5% estimated total injection loss. For short filter cavities, in which the separation between input and output beams is significant in a bow-tie geometry (C), the coupling to a countercirculating mode may be negligible, and the absence of an optical isolator will make this option preferable.

Figure 6

An input filter cavity could be included in the existing vacuum envelope of Advanced LIGO. The seismically isolated tables shown in this figure contain the interferometer output optics and offer a 16 m baseline with superior vibration isolation and direct access to the Faraday isolator with which the squeezed vacuum will be injected. Acronyms used in the figure are signal recycling mirror (SRM), filter cavity input mirror (FC1), and filter cavity end mirror (FC2).