  Amplification of light through stimulated emission or nonlinear optical
interactions has had a transformative impact on modern science and technology.
The amplification of other bosonic excitations, like phonons in solids, is
likely to open up new remarkable physical phenomena. Here, we report on an
experimental demonstration of optical phonon amplification. A coherent
mid-infrared optical field is used to drive large amplitude oscillations of the
Si-C stretching mode in silicon carbide. Upon nonlinear phonon excitation, a
second probe pulse experiences parametric optical gain at all wavelengths
throughout the reststrahlen band, which reflects the amplification of
optical-phonon fluctuations. Starting from first principle calculations, we
show that the high-frequency dielectric permittivity and the phonon oscillator
strength depend quadratically on the lattice coordinate. In the experimental
conditions explored here, these oscillate then at twice the frequency of the
optical field and provide a parametric drive for lattice fluctuations.
Parametric gain in phononic four wave mixing is a generic mechanism that can be
extended to all polar modes of solids, as a new means to control the kinetics
of phase transitions, to amplify many body interactions or to control
phonon-polariton waves.
