  We study unconventional cavity optomechanics and the acoustic analogue of
radiation pressure to show the possibility of nonlinear coherent control of
phonons in the acoustic quantum vacuum. Specifically, we study systems where a
quantized optical field effectively modifies the frequency of an acoustic
resonator. We present a general method to enhance such a nonlinear interaction
by employing an intermediate qubit. Compared with conventional optomechanical
systems, the roles of mechanical and optical resonators are interchanged, and
the boundary condition of the phonon resonator can be modulated with an
ultrahigh optical frequency. These differences allow to test some quantum
effects with parameters which are far beyond the reach of conventional cavity
optomechanics. Based on this novel interaction form, we show that various
nonclassical quantum effects can be realized. Examples include an effective
method for modulating the resonance frequency of a phonon resonator (e.g., a
surface-acoustic-wave resonator), demonstrating mechanical parametric
amplification, and the dynamical Casimir effect of phonons originating from the
acoustic quantum vacuum. Our results demonstrate that unconventional
optomechanics offers a versatile hybrid platform for quantum engineering of
nonclassical phonon states in quantum acoustodynamics.
