Mechanical loss of a multilayer tantala/silica coating on a sapphire disk at cryogenic temperatures: Toward the KAGRA gravitational wave detector

We report the results of a new experimental setup to measure the mechanical loss of coating layers on a thin sapphire disk at cryogenic temperatures. Some of the authors previously reported that there was no temperature dependence of the mechanical loss from a multilayer tantala/silica coating on a sapphire disk, both before and after heat treatment, although some reports indicate that ${\mathrm{Ta}}_2{\mathrm{O}}_5$ and ${\mathrm{SiO}}_2$ layers annealed at $600°\mathrm{C}$ have loss peaks near 20 K. Since KAGRA—the Japanese gravitational-wave detector, currently under construction—will be operated at 20 K and have coated sapphire mirrors, it is very important to clarify the mechanical loss behavior of tantala/silica coatings around this temperature. We carefully investigate a tantala/silica-coated sapphire disk with the new setup, anneal the disk, and then investigate the annealed disk. We find that there is no distinct loss peak both before and after annealing under particular conditions. The mechanical loss for the unannealed disk at 20 K is about $5\times {10}^{-4}$, as previously reported, while that for the annealed disk is approximately $6.4\times {10}^{-4}$.

Figure 1

The sapphire disk is clamped at the center and an electrode is bolted onto the top plate so that the clearance between the disk and the electrode is adjustable. The body, made of copper, has a heater on the top plate to accurately control the disk temperature, and three thermometers are attached to monitor the disk temperature. The body is placed inside a cryostat, and the motion of the disk is monitored using an optical lever.

Figure 2

The disk temperature was calibrated against the top-plate temperature when the heater was switched on. We fitted the result with a polynomial function, and $dT$ is the deviation between the measured points and the polynomial function. Below 30 K, $dT$ is less than 0.1 K.

Figure 3

Spectrum analyzer output of QPD signal at 28 K. “Dark” represents the case when no laser light hits the QPD, where the harmonics from the power line are apparent. The blue line shows the frequency spectrum of a typical excited resonant mode of the disk. The excited quadrupole mode is the only strong signal in the frequency range. The electrode bolted onto the top plate vibrates and the motion appears in the signal.

Figure 4

Blue circles and green squares indicate the unannealed coated and uncoated disks, respectively. The black dashed line shows the thermoelastic loss. The quality factor was measured three times at each temperature, and the points and error bars in the plot represent the average and standard deviation, respectively.

Figure 5

Blue circles show the mechanical losses of the unannealed coated disk (mode 1) and black squares show those in Ref. [24]. The other results are for the annealed coated disk at three different frequencies: 521 Hz (mode 1, red crosses), 1204 Hz (mode 2, green squares), and 4594 Hz (mode 4, cyan triangles). The unannealed disk reproduced the same temperature-independent behavior as previously observed, and the annealed disk also did not have any apparent peaks below 50 K.

Figure 6

Dark-field images of disks annealed at $600°\mathrm{C}$ (upper) and $500°\mathrm{C}$ (lower). The latter disk was investigated in this study, and a zoomed bright-field image is also shown. Although the defect density is very small, in the disk annealed at $500°\mathrm{C}$, similar defects to those appearing in the upper disk were observed.