  We demonstrate low-power amplification process in cavity optomechanics (COM).
This operation is based on the nonlinear position-modulated self-Kerr
interaction. Owing to this nonlinear term, the effective coupling highly scales
with the photon number, resulting in a giant enhancement of the cooperativity.
Even for small nonlinearity, the system reaches the amplification threshold for
weak driving strength, leading to low-power phonon lasing. This amplifier can
be phase-preserving and provides a practical advantage related to the power
consumption issues. This work opens up new avenues to realize low-power and
efficient amplifiers in optomechanics and related fields.
