Optimizing gravitational-wave detector design for squeezed light

Achieving the quantum noise targets of third-generation detectors will require 10 dB of squeezed-light enhancement as well as megawatt laser power in the interferometer arms—both of which require unprecedented control of the internal optical losses. In this work, we present a novel optimization approach to gravitational-wave detector design aimed at maximizing the robustness to common, yet unavoidable, optical fabrication and installation errors, which have caused significant loss in Advanced LIGO. As a proof of concept, we employ these techniques to perform a two-part optimization of the LIGO $\mathrm{A}+$ design. First, we optimize the arm cavities for reduced scattering loss in the presence of point absorbers, as currently limit the operating power of Advanced LIGO. Then, we optimize the signal recycling cavity for maximum squeezing performance, accounting for realistic errors in the positions and radii of curvature of the optics. Our findings suggest that these techniques can be leveraged to achieve substantially greater quantum noise performance in current and future gravitational-wave detectors.

Figure 1

Proposed surface profiles for the LIGO $\mathrm{A}+$ input test masses (ITM; left) and end test masses (ETM; right). In each panel, the total surface figure (pink curve) is the sum of the polishing profile (blue curve) and the optical coating nonuniformity (gray curve). Based on current fabrication capabilities, the polishing slope is restricted to $\le 2.5\mathrm{nm}/\mathrm{mm}$, as shown in the lower panels.

Figure 2

Optical gain $g_{mn}$ of the 7th-order Laguerre-Gauss (LG) modes in the LIGO $\mathrm{A}+$ arm cavities, as a function of frequency detuning from the fundamental mode resonance. Top: the nominal resonance locations with a spherical test mass polish. Bottom: the new resonance locations after including the compensation polish shown in Fig. 1 (blue curves). In both panels, coating absorption of 120 mW per test mass is assumed.

Figure 3

Arm cavity loss as a function of mode order. Each curve represents the median loss in 1000 trials with random miscenterings and surface roughnesses, averaged over all Laguerre-Gauss modes ${\mathrm{LG}}_{p,l}$ of order $N=2p+|l|$. The shading represents the 16th and 84th percentiles of the loss distributions over all trials and modes. The proposed mirror profiles achieve significantly enhanced higher-order mode dissipation, with no increase in fundamental mode loss.

Figure 4

Arm cavity loss distributions due to point absorbers, shown at three different power levels. Each loss distribution represents 1000 trials with a point absorber randomly positioned on each test mass. Uniform coating absorption of 0.3 ppm per test mass, along with optimal ring heater compensation, is assumed.

Figure 5

Optical configuration used for simulating a LIGO-like interferometer. All of the distances and radii of curvature are fixed to the nominal LIGO A+ design values, except for the signal recycling cavity parameters which are indicated in blue.

Figure 6

Nominal versus optimized signal recycling cavity designs for LIGO $\mathrm{A}+$. Shown is the Gaussian beam size (top) and the accumulated Gouy phase (bottom) along the cavity axis, from the ITM to the SRM. Of all the optics, only the positions of SR2 and SR3 are allowed to vary.

Figure 7

Probability distributions of the squeezing achieved with two different signal recycling cavity (SRC) designs, in the presence of realistic random optical errors. The three panels assume various levels of readout loss ranging from 5% (top) to 20% (bottom). In each panel, the black vertical lines indicate the difference in worst possible outcome, at 95% confidence, between the two designs.

Figure 8

Corner plot comparing the sensitivity to error in pairs of parameters (see Table 1) between two signal recycling cavity (SRC) designs. In each panel, the lines represent iso-squeezing contours at which errors in the two parameters degrade the observed squeezing by 3 dB, compared to the unperturbed case (located at the origin). A larger area enclosed by the iso-squeezing contour of one design indicates a greater error tolerance.