[Abe, Ushiba, Tanaka, Komori]

Abstract:

We measured the violin mode Q-values of sapphire fibers at EX, IX, and IY using ringdown measurements.
The estimated Q-values are 1.6e4, 1.5e4, and 1.8e4, respectively.
In comparison, line width measurements suggest Q-values of 1.4e4, 1.7e4, and 1.8e4.
The results from the two methods are consistent within 15% accuracy.

Details:

We conducted ringdown measurements following the same procedure as reported in klog:31963, targeting the sapphire fibers at EX, IX, and IY.
Sine waves at the resonant frequencies of each violin mode were injected into the channels VIS-{ETMX, ITMX, ITMY}_IM_TEST_P_EXC with an amplitude of 3 counts for 10–20 seconds.
The excitation was then stopped to observe the ringdown behavior.

The selected resonant frequencies were 184.562 Hz (EX), 174.047 Hz (IX), and 176.504 Hz (IY).
Fitting the ringdown data yielded Q-values of 1.6e4, 1.5e4, and 1.8e4, respectively (Fig. 1–3).

On the other hand, line width measurements indicated Q-values of 1.4e4, 1.7e4, and 1.8e4, respectively (Fig. 4).
The differences between the two methods are within approximately 15%, including the results from previous EY measurements.

Conclusion:

These results demonstrate that ringdown measurements and line width measurements are consistent within a reasonable accuracy of 15%.
This causes the error of only 8% for estimation of the thermal noise in the amplitude spectral density.
Therefore, it is not necessary to measure Q-values using the ringdown method at 250 K, where the thermo-elastic loss is the dominant factor, with Q-values at the level of 1e4.
Instead, the line width measurement is sufficient for this purpose.