Coulomb-interaction-dependent effect of high-order sideband generation in an optomechanical system

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 charge number, the 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.

Figure 1

Schematic diagram of an optomechanical system where the MR is charge coupling to an adjoining charged body. The optomechanical system is driven by a strong pump field with frequency ${\omega }_1$ and the weak probe field with frequency ${\omega }_p$. The output field is represented by ${\varepsilon }_{\mathrm{out}}$. Through the control of the strength of the driving field and the charge, we can get different features of the output high-order sidebands spectrum.

Figure 2

The displacement $x_s$ as function of the power of the control field and charge number. The parameters are ${\mathrm{\Delta }}_c={\omega }_m=\delta , {\lambda }_c\equiv 2\pi c/{\omega }_c=$ 1064 nm, $G/2\pi =-11$ MHz/nm, $m=145$ ng, $\kappa /2\pi =215$ kHz, ${\omega }_m/2\pi =947$ kHz, ${\gamma }_m/2\pi =141$ Hz, $r=67\mu \mathrm{m}$, and $Q_1=CU$ with $C=27.5$ nF and $U=1$ V [13].

Figure 3

Frequency spectra output from the optomechanical system is shown with various charge number. The frequency spectra output shift a frequency ${\omega }_1$ due to the evolution of the cavity field in a frame rotating at the frequency ${\omega }_1$. We use ${\varepsilon }_p={\varepsilon }_1/2$. The power of the control field is $P_1=10$ mW and the charge number vary from 0, 10, 33, to 80 in (a), (b), (c), and (d), respectively.

Figure 4

(a) Frequency spectra output from the optomechanical system without Coulomb force. (b) The amplitudes of high-order sideband generation with different charge number from 0 to 9. The power of the control field is 20 mW and we use ${\varepsilon }_p={\varepsilon }_1/2$.