Optical probing of mechanical loss of a Si₃N₄ membrane below 100 mK

We report on low mechanical loss in a high-stress silicon nitride (Si_{3}N_{4}) membrane at temperatures below 100 mK. We isolate a membrane via a phononic shield formed within a supporting silicon frame, and measure the mechanical quality factor of a number of high-tension membrane modes as we vary our dilution refrigerator base temperature between 35 mK and 5 K. At the lowest temperatures, we obtain a maximum quality factor (Q) of 2.3\times10^{8}, corresponding to a Q-frequency product (QFP) of 3.7\times10^{14} Hz. These measurements complement the recent observation of improved quality factors of Si_{3}N_{4} at ultralow temperatures via electrical detection. We also observe a dependence of the quality factor on optical heating of the device. By combining exceptional material properties, high tension, advanced isolation and clamping techniques, high-stress mechanical objects are poised to explore a new regime of exceptional quality factors. Such quality factors combined with an optical probe at cryogenic temperatures will have a direct impact on resonators as quantum objects, as well as force sensors at mK temperatures.