Jie-Qiao Liao, Franco Nori
We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in \emph{quadratically}-coupled optomechanics. We consider the single-photon emission when the photon is initially inside the cavity. We also consider the single-photon scattering when the photon wavepacket is initially in the fields outside the cavity. Using our solutions, we calculate the single-photon emission and scattering spectra, and build the connection between the spectral features and the system's inherent parameters, such as: the coupling strength, the mechanical frequency, and the cavity decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible.
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http://arxiv.org/abs/1304.6612
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