The cantilever was fully cooled by the time I got in this afternoon. I measured some quick ringdowns by looking at the amplitude on the scope, and estimated a Q of 2-2.5 x 104. This is slightly better than what I measured the other day before improving the clamping (see CRYO:1193), but not good---still a few orders of magnitude below what we expect. I heated the system up near 120 K and found a slight reduction in Q.
Unlike before, I noticed a strange sort of sloshing of energy into a higher-frequency mode (~1350 Hz). It was hard to tell, but I got the sense that energy was being dissipated out of the fundamental mode through this higher-order one. I looked at a time-lapse spectrum of the ringdown, and it seemed to confirm this effect. If you look at the movie below (which is just about real time), you can see that the RMS of the two modes between 1-2 kHz pump up and down, while the fundamental mode around 215 Hz monotonically decreases. If you squint, it appears that the full RMS stays constant in most cases while the high-frequency modes ring up, while they all decrease together. This, coupled with the fact that everything rings down to zero if left alone, indicates to me that energy is leaking from the fundamental mode out through these others. As an order-of-magnitude estimate, the amount of energy pumped through these modes as the amplitudes increase and decrease is not inconsistent with the energy lost from the fundamental based on the observed Q.
I did some COMSOLing to try and figure out what is going on, and at first I couldn't explain it; it appeared that even the higher-frequency modes should have too little strain energy density leakage into the steel to explain the effect, especially with the sapphire spacers. In looking a little more carefully, though, I realized that we have not been careful enough in modeling our system: at the bottom of the clamp stack, there is a PEEK platform between the clamp post and the cold plate. This is there by design, to thermally insulate the clamp from the bath (for heating), but it also considerably softens the contact there.
This PEEK piece shouldn't have much of an effect on the fundamental mode, as the energy ratio for that mode is of order 10-4. The second mode at 1350 Hz is nearly as well isolated. However, for the third mode around 1800 Hz, something like 70%(!!) of the energy is expected to reside in the PEEK layer. Since PEEK has very high loss, this is not good. Here are some COMSOL screenshots, with the first 3 showing the first 3 mode shapes, and the fourth showing the (log) strain energy density for the 3rd mode. Note that this model is run at room temperature, so the eigenfrequencies are somewhat higher than in my spectra.
So, my hypothesis is that somehow energy is leaking from the (otherwise well-isolated) fundamental mode into these higher-order ones, where it is immediately lost to friction in the PEEK. One possible step is to get rid of the PEEK piece, but that doesn't address the question of why the cross-coupling exists in the first place. My intuition fails me, so I'm not sure what the right thing to do is.