二次光力耦合与参量放大器对本征模劈裂的影响

Normal-mode Splitting in the Optomechanical System:Effect of Quadratic Coupling and the Parametric Amplifier

本文基于一个含有光学参量放大器的腔光力系统,其中腔场和机械场之间具有线性和二次色散耦合的相互作用,研究了二次光力耦合与参量放大器对本征模劈裂的重要影响。通过分析腔场涨落项的输出谱和机械振子位移的涨落谱,得出结论:腔场和机械场均呈现出本征模劈裂的现象,光学参量放大器非线性增益值的大小及二次光力耦合强度均正比于劈裂谱两峰之间的距离,即二者对本征模劈裂效应具有相似的调控作用。本文同时也验证了文献[Journal of Modern Optics,66(5):494–501(2019)]的结论:具有线性和二次耦合的光力系统可以是含有光学参量放大器混合光力系统的一个替代研究平台。

The normal-mode splitting in the optomechanical systems has attracted widely attention.This behavior of mode splitting arises due to the strong interaction between the oscillator and optical light circulating inside the cavity,when the system is in the resolved side band regime.Recently,many methods are proposed to produce the larger splitting by increasing the optomechanical coupling.It is proved that the observation of the normal-mode splitting is more accessible by placing the optical parametric amplifier inside the cavity,which is due mainly to the increase of the coupling between the oscillator and the cavity field.On the other hand,quadratic coupling can also increase the effective optomechanical coupling.Our paper is based on the above general background,and we study the important influence of quadratic optomechanical coupling and the parametric amplifier on normal-mode splitting in the optomechanical system with both linear and quadratic dispersion coupling.To investigate the normal-mode splitting effect,we calculate the output spectrum of the cavity and the spectrum of the mechanical oscillator displacement.Then,the calculated spectrum is plotted as a function of normalized frequency.The output spectrum of the cavity and the mechanical oscillator’s position spectrum all exhibit the double-peak structure.Thus,we can obtain the conclusions that both the cavity field and the mechanical field have normal-mode splitting behaviors.Further analysis of width of the normal-mode splitting peaks is analysed by discussing the spectra with different quadratic couplings and the parametric gain values.We find that the width of double-peak structure of the spectrum is increasing with the quadratic coupling,as well as the parametric gain.The physical explanation leading to such a phenomenon is that the increasing of quadratic coupling and the parametric gain aids in producing more number of cavity photons.As a result,this also leads to the increasing in effective optomechanical coupling.Quadratic coupling and the parametric gain have similar effects on the normal-mode splitting.In other words,the the normal-mode splitting behavior can be controlled by quadratic coupling or the parametric gain.Thus,It also proves the conclusion of the reference[Journal of Modern Optics 66(5):494–501(2019)]that the optomechanical systems with linear coupling and quadratic coupling can be seen as a alternative platforms to hybrid-optomechanical systems with the parametric amplifier.