Cavity nano-optomechanics with suspended subwavelength-sized nanowires

In the field of cavity nano-optomechanics, the nanoresonator-in-the-middle approach consists in inserting a sub-wavelength sized deformable resonator, here a nanowire, in the small mode volume of a fiber microcavity. Internal resonances in the nanowire enhance the light nanowire interaction which provide giant coupling strengthes -- sufficient to enter the single photon regime of cavity optomechanics -- at the condition to precisely position the nanowire within the cavity field. Here we expose a theoretical description that combines an analytical formulation of the Mie-scattering of the intracavity light by the nanowire and an input-output formalism describing the dynamics of the intracavity optical eigenmodes. We investigate both facets of the optomechanical interaction describing the position dependent parametric and dissipative optomechanical coupling strengths, as well as the optomechanical force field experienced by the nanowire. We find a quantitative agreement with recent experimental realization. We discuss the specific phenomenology of the optomechanical interaction which acquires a vectorial character since the nanowire can identically vibrate along both transverse directions: the optomechanical force field presents a non-zero rotational, while anomalous positive cavity shifts are expected. Taking advantage of the large Kerr-like non linearity, this work opens perspectives in the field of quantum optics with nanoresonator with for instance broadband squeezing of the outgoing cavity fields close to the single photon level.