  Adding excitations on a coherent state provides an effective way to observe
nonclassical properties of radiation fields. Here we describe and analyse how
to apply this concept to the motional state of a mechanical oscillator and
present a full scheme to prepare non-Gaussian {\it phonon}-added coherent
states of the mechanical motion in cavity optomechanics. We first generate a
mechanical coherent state using electromagnetically induced transparency. We
then add a single phonon onto the coherent state via optomechanical parametric
down-conversion combined with single photon detection. We validate this
single-phonon-added coherent state by using a red-detuned beam and reading out
the state of the optical output field. This approach allows us to verify
nonclassical properties of the phonon state, such as sub-Poissonian character
and quadrature squeezing. We further show that our scheme can be directly
implemented using existing devices, and is generic in nature and hence
applicable to a variety of systems in opto- and electromechanics.
