  The coupling of distinct systems underlies nearly all physical phenomena and
their applications. A basic instance is that of interacting harmonic
oscillators, which gives rise to, for example, the phonon eigenmodes in a
crystal lattice. Particularly important are the interactions in hybrid quantum
systems consisting of different kinds of degrees of freedom. These assemblies
can combine the benefits of each in future quantum technologies. Here, we
investigate a hybrid optomechanical system having three degrees of freedom,
consisting of a microwave cavity and two micromechanical beams with closely
spaced frequencies around 32 MHz and no direct interaction. We record the first
evidence of tripartite optomechanical mixing, implying that the eigenmodes are
combinations of one photonic and two phononic modes. We identify an asymmetric
dark mode having a long lifetime. Simultaneously, we operate the nearly
macroscopic mechanical modes close to the motional quantum ground state, down
to 1.8 thermal quanta, achieved by back-action cooling. These results
constitute an important advance towards engineering entangled motional states.
