  In recent years, nanomechanical oscillators in thin films of superfluid
helium have attracted attention in the field of optomechanics due to their
exceptionally low mechanical dissipation and optical scattering. Mechanical
excitations in superfluid thin films - so-called third sound waves - can
interact with the optical mode of an optical microresonator by modulation of
its effective refractive index enabling optomechanical coupling. Strong
confinement of third sound modes enhances their intrinsic mechanical
non-linearity paving the way for strong phonon-phonon interactions with
applications in quantum optomechanics. Here, we realize a phononic crystal
cavity confining third sound modes in a superfluid helium film to length scales
close to the third sound wavelength. A few nanometer thick superfluid film is
self-assembled on top of a silicon nanobeam optical resonator. The periodic
patterning of the silicon material creates a periodic modulation of the
superfluid film leading to the formation of a phononic band gap. By engineering
the geometry of the silicon nanobeam, the phononic band gap allows the
confinement of a localized phononic mode.
