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Adding excitations on a coherent state provides an effective way to observenonclassical properties of radiation fields. Here we describe and analyse howto apply this concept to the motional state of a mechanical oscillator andpresent a full scheme to prepare non-Gaussian {\it phonon}-added coherentstates of the mechanical motion in cavity optomechanics. We first generate amechanical coherent state using electromagnetically induced transparency. Wethen add a single phonon onto the coherent state via optomechanical parametricdown-conversion combined with single photon detection. We validate thissingle-phonon-added coherent state by using a red-detuned beam and reading outthe state of the optical output field. This approach allows us to verifynonclassical properties of the phonon state, such as sub-Poissonian characterand quadrature squeezing. We further show that our scheme can be directlyimplemented using existing devices, and is generic in nature and henceapplicable to a variety of systems in opto- and electromechanics.

Generation and detection of non-Gaussian phonon-added coherent states in optomechanical systems