  Optomechanical systems couple an electromagnetic cavity to a mechanical
resonator which is typically formed from a solid object. The range of phenomena
accessible to these systems depends on the properties of the mechanical
resonator and on the manner in which it couples to the cavity fields. In both
respects, a mechanical resonator formed from superfluid liquid helium offers
several appealing features: low electromagnetic absorption, high thermal
conductivity, vanishing viscosity, well-understood mechanical loss, and in situ
alignment with cryogenic cavities. In addition, it offers degrees of freedom
that differ qualitatively from those of a solid. Here, we describe an
optomechanical system consisting of a miniature optical cavity filled with
superfluid helium. The cavity mirrors define optical and mechanical modes with
near-perfect overlap, resulting in an optomechanical coupling rate ~3 kHz. This
coupling is used to drive the superfluid; it is also used to observe the
superfluid's thermal motion, resolving a mean phonon number as low as 11.
