Feedback Cooling Of The Si₃N₄ Membrane Mechanical Resonators In The Unresolved Sideband Cavity Optomechanical System

Cavity optomechanics is a developing research field,which mainly studying the coupling between the radiation pressure of light and the mechanical motion[1].In recent years,benefiting from the mature of the micro/nano fabrication,cavity optomechanics has a rapid development and application.First,cavity mechanical system could apply a unique platform for the study of the quantum optics in macroscopic mechanical resonators.And then cavity optomechanics could play important roles in the measurement of the tiny displacement and the weak force,it could even been used in the detection of gravitational waves.At present,as a consequence of the influence of the environment thermal noise,mechanical motion could not enter the quantum region.To address this problem,our group carried out the experimental study on the ground cooling of the mechanical mode of the membrane resonators.The main content is divided into the following three parts:First,giving an introduction of the membrane in cavity optomechanical system which was used in our experimental research,including the basic performance of the high finesse F-P cavity and the membrane resonators,and construction of the membrane in the middle cavity optomechanical system.We also analyzed the theoretical optomechanical interaction model.Second,we have designed the cascaded on-chip phonon shield for membrane resonators to reduce the phonon tunneling loss and derived a theoretical model for the structure.We measured the frequency response of the cascaded phonon shield and got the 30 d B mechanical isolation.Thus we reliably fabricate Si₃N₄ membrane resonators with mechanical quality factor of around 2×10⁶ at room temperature.Third,we have derived and theoretical simulated the feedback cooling model of the membrane cavity optomechanics in the unresolved sideband regime.We applied a feedback force which was inversely proportional to the motion of membrane,by modulating amplitude of the incident light field,to cool the mechanical mode of the membrane.Finally,we have completed the feedback cooling experiment at room temperature,and reduced the phonon number of the（1,1）mode within 200.