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High-order sideband generation in an optomechanical system coupled to a charged object is discussed, and the features of Coulomb-interaction dependent effect are identified. We show that the Coulomb-interaction dependent effect of high-order sideband generation exhibits essential difference between the case of weak control field and strong control field. In the weak control field case, the output spectra are in the perturbative regime and there is hardly any Coulomb-interaction dependent effect in an optomechanical system coupling to an object with a small amount of charge. In the strong control field case, the output spectra are in the nonperturbative regime and robust Coulomb-interaction dependent effect arises even if there are few charges. The amplitudes of specific sidebands are also discussed, and it is shown that Coulomb interaction plays an important role in achieving optomechanical control. Due to the extremely sensitive to charge number, Coulomb-interaction dependent effect of high-order sideband generation is remarkable in many aspects and may be used to precision measurement of electrical charges beyond the linearized optomechanical interaction.

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Recent research on parity-time- (𝒫𝒯-) symmetric optical structures have exhibited great potential for achieving distinctive optical behaviour which is unattainable with ordinary optical systems. Here we propose a 𝒫𝒯-symmetric cavity-magnon system consisting of active cavity mode strongly interacting with magnon to study magnon-induced transparency (MIT) and amplification (MIA) by exploiting recent microwave-cavity-engineered ferromagnetic magnons. We find that (i) due to the gain-induced enhancement of coherent coupling between the cavity field and the magnon, the transmitted probe power is remarkably enhanced about four orders of magnitude and the bandwidth also becomes much narrower, compared to passive cavity system. (ii) More importantly, the light transmission can be well controlled by adjusting the applied magnetic field without changing other parameters, and a Lorentzian-like spectra can be established between the transmitted probe power and the external magnetic field, which provides an additional degree of freedom to realize the coherent manipulation of optical transparency and amplification. Our results may offer an approach to make a low-power magnetic-field-controlled optical amplifier in 𝒫𝒯-symmetric cavity-magnon system.