Cavity Optomechanics in Solid Helium and Solid Neon

Cavity optomechanical systems have been used to realize highly sensitive metrological devices and are also proposed as a tool for studying questions in fundamental physics [1,2]. We have previously demonstrated an optomechanical system using an optical fiber cavity filled with superfluid He [3,4], in which an optical mode (wavelength = 1550 nm) couples to an acoustic mode of the superfluid with precisely half the wavelength. This acoustic mode has a resonance frequency of 320 MHz, and so is cooled to a mean phonon number ~ 1 in a conventional dilution refrigerator. Here we look at the feasibility of using solid He and Ne crystals as the medium in such cavities, as their greater sound velocity will result in 1550 nm light coupling to acoustic modes at 600 MHz and 1.4 GHz respectively. As the crystals are acoustically anisotropic, we use the Christoffel equation and finite element simulations to find the acoustic eigenmodes of the cavity. The spatial profiles of these eigenmodes depend on the angle between the crystal axis with the cavity axis. We find that for a range of crystal orientations, there exist eigenmodes whose spatial profiles closely resemble a Gaussian. These acoustic eigenmodes are predicted to have a high degree of overlap with the optical Gaussian mode, and thus are good candidates to realize a large optomechanical coupling.