Trade-off between quantum and thermal fluctuations in mirror coatings yields improved sensitivity of gravitational-wave interferometers

We propose a simple way to improve the sensitivity of laser gravitational-wave detectors and other high-precision laser interferometric position meters by means of reduction of the number of reflective coating layers of the core optics mirrors. This effects in the proportional decrease of the coating thermal noise, the most notorious among the interferometer’s technical noise sources. The price for this is increased quantum noise, as well as high requirements for the pump laser power and, therefore, power at the beam splitter, the power-recycling mirror, and the arm cavities’ input mirror substrates. However, as far as these processes depend differently on the coating thickness, we demonstrate that a certain trade-off is possible. In the particular case of large-scale laser gravitational-wave detectors, this trade-off yields a 20–30% gain (for diverse gravitational-wave signal types and interferometer configurations), provided that increased laser power (comparable with that planned for the third-generation gravitational-wave detectors) becomes available, and that it will be possible to mitigate the increased thermal effects caused by absorption in the beam splitter and input mirrors.

Figure 1

The schemes of the advanced gravitation-wave detector being considered in this paper. Top left: The signal- and power-recycled interferometer similar to the one planned for Advanced LIGO [35] (referred to as “plain”). Top right: The configuration with frequency-independent squeezed light injection into the dark port (referred to as “squeezed”). Bottom left: The configuration with injection of frequency-dependent squeezed light created by means of the input filter cavity (referred to as “prefiltering”). Bottom right: The back-action-evading configuration with the additional output filter cavity and the squeezed light injection into the dark port (referred to as “postfiltering”).

Figure 2

Relative gain in SNR as a function of the coating-layer doublet numbers $N_{\mathrm{ITM}}$, $N_{\mathrm{ETM}}$. Cyan and magenta dots correspond to the default numbers $N_{\mathrm{ITM}}^{\mathrm{def}}=8$, $N_{\mathrm{ETM}}^{\mathrm{def}}=19$ given by GWINC. The red dot marks the maximum signal-to-noise ratio given the technical limitations on the total power absorbed in the core optics discussed in Sec. 2c.

Figure 3

Optimal quantum and technical noise spectral densities for the BNS sources. Left column: Schemes with frequency-independent squeezing (referred to as “squeezed”). Right column: Schemes with frequency-dependent input squeezing (referred to as “prefiltering”). Top row: $I_c=200\mathrm{kW}$; bottom row: $I_c=840\mathrm{kW}$. Solid lines: Optimized numbers of the coating-layer doublets $N_{\mathrm{ITM}}$ and $N_{\mathrm{ETM}}$. Dashed lines: Default numbers $N_{\mathrm{ITM}}=8$ and $N_{\mathrm{ETM}}=19$. Dash-dotted line: “Baseline” configuration: $I_c=840\mathrm{kW}$, $N_{\mathrm{ITM}}=8$ and $N_{\mathrm{ETM}}=19$, no squeezing. Dotted line: SQL.

Figure 4

Optimal quantum and technical noise spectral densities for the burst sources. Left column: Schemes with frequencyindependent squeezing (referred to as “squeezed”). Right column: Schemes with frequency-dependent input squeezing (referred to as “prefiltering”). Top row: $I_c=200\mathrm{kW}$; bottom row: $I_c=840\mathrm{kW}$. Solid lines: Optimized numbers of the coating-layer doublets $N_{\mathrm{ITM}}$ and $N_{\mathrm{ETM}}$. Dashed lines: Default numbers $N_{\mathrm{ITM}}=8$ and $N_{\mathrm{ETM}}=19$. Dash-dotted line: “Baseline” configuration: See Eq. (9). Dotted line: SQL.