title: Single-photon quadratic optomechanics.
abstract: We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon.
authors.affiliation: CEMS, RIKEN, Saitama 351-0198, Japan.
authors.forename: Jie-Qiao
authors.initials: JQ
authors.lastname: Liao
authors.affiliation: 1] CEMS, RIKEN, Saitama 351-0198, Japan [2] Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
authors.forename: Franco
authors.initials: F
authors.lastname: Nori