Normal-mode splitting in a coupled system of a nanomechanical oscillator and a parametric amplifier cavity

We study how an optical parametric amplifier inside the cavity can affect the normal-mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.