Exploring the Macroscopic Quantum Physics of Motion with Superfluid He-4

We demonstrate the use of superfluid helium-4 as an extremely low loss optomechanical element. We form an optomechanical system with a cylindrical niobium superconducting TE$_{011}$ resonator whose 40 cm$^3$ inner cylindrical cavity is filled with $^4$He. Coupling is realized via the variations in permittivity resulting from the density profile of the acoustic modes. Acoustic losses in helium-4 below 500 mK are governed by the intrinsic nonlinearity of sound, leading to an attenuation which drops as T$^4$, indicating the possibility of quality factors (Q) over 10$^{10}$ at 10 mK. In our lowest loss mode, we demonstrate this T$^4$ law at temperatures down to 50 mK, realizing an acoustic Q of 1.35*10$^8$ at 8.1 kHz. When coupled with a low phase noise microwave source, we expect this system to be utilized as a probe of macroscopic quantized motion, for precision measurements to search for fundamental physical length scales, and as a continuous gravitational wave detector. Our estimates suggest that a resonant superfluid acoustic system could exceed the sensitivity of current broad-band detectors for narrow-band sources such as pulsars.\\ \\ De Lorenzo, L. A. and Schwab, K. C., \emph{New J. Phys.} \textbf{16}, 113020 (2014).