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We propose an efficient scheme for the controllable amplification of two-phonon higher-order sidebands in a quadratically coupled optomechanical system. In this scheme, a strong control field and a weak probe pulse are injected into the cavity, and the membrane located at the middle position of the cavity is driven resonantly by a weak coherent mechanical pump. Beyond the conventional linearized approximation, we derive analytical expressions for the output transmission of probe pulse and the amplitude of second-order sideband by adding the nonlinear coefficients into the Heisenberg-Langevin formalism. Using experimentally achievable parameters, we identify the conditions under which the mechanical pump and the frequency detuning of control field allow us to modify the transmission of probe pulse and improve the amplitude of two-phonon higher-order sideband generation beyond what is achievable in absence of the mechanical pump. Furthermore, we also find that the higher-order sideband generation depends sensitively on the phase of mechanical pump when the control field becomes strong. The present proposal offers a practical opportunity to design chip-scale optical communications and optical frequency combs.

We propose an efficient scheme to generate quadrature squeezing of a higher-order sideband spectrum in an optomechanical system. This is achieved by exploiting a well-established optomechanical circumstance, where a second-order nonlinearity is embedded into the optomechanical cavity driven by a strong control field and a weak probe pulse. Using experimentally achievable parameters, we demonstrate that the second-order nonlinearity intensity and the frequency detuning of a control field allow us to modify the amplitude of higher-order sidebands and improve the amount of squeezing of a higher-order sideband spectrum. Furthermore, in the presence of a strong second-order nonlinearity, an optimizing quadrature squeezing of a higher-order sideband spectrum can be achieved, which provides a practical opportunity to design the squeezed frequency combs and other precision measurements.

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We propose a potentially practical scheme for realizing ultrasensitive size sensor of a single metallic nanoparticles (MNP) in a hybrid nonlinear microcavity. This is achieved by exploiting a well-established microcavity-engineered plasmonic resonance, where a degenerate parametric amplifier (DPA) is embedded into the microcavity driven by a strong pump field and a weak probe pulse. It is shown that the transmission spectrum of the probe pulse exihibits a two-peak splitting and the splitting width depends on the radius. The radius of a single MNP can be inferred from the transmission spectrum by monitoring the width between two peaks. Using experimentally achievable parameters, we identify the detection sensitivity of the sensor can reach approximately 0.198 THz/nm for detecting and sizing of individual MNPs as small as 10 nm in radius.