  The widespread availability of quantum entanglement with photons, in the
guise of two-mode squeezed states, can be attributed to the phenomenon of
parametric down-conversion. A reinterpretation of this effect with macroscopic
mechanical objects can offer a route towards a purely mechanical entanglement
and the unique possibility of probing the quantum mechanical nature of our
everyday classical world. In spite of this prospect, mechanical two-mode
squeezed states have remained elusive due to the inability to recreate the
nonlinear interaction at the heart of this phenomenon in the mechanical domain.
To address this we have developed a parametric down-converter, in a mechanical
resonator integrated with electrical functionality, which enables mechanical
nonlinearities to be dynamically engineered to emulate the parametric
down-conversion interaction. In this configuration, phonons are simultaneously
generated in pairs in two macroscopic vibration modes which results in the
amplification of their motion. In parallel, mechanical two-mode squeezed states
are also created which exhibit fluctuations far below the thermal level of
their constituent modes as well as harbouring correlations between the modes
that become almost perfect as their amplification is increased. This remarkable
observation of correlations between two massive phonon ensembles paves the way
towards an entangled macroscopic mechanical system at the single phonon level.
