Multimode Optomechanics And Precision Measurement Based On Nanomechanical Membranes

The momentum of the photon brings radiation pressure and thus exert the mechanical effect on material objects.The interaction between the light and the mechanical oscillator is the main topic of optomechanics.Cavity optomechanics has attracted considerable attention due to its wide applications in highly sensitive measurements,quantum information,quantum computing,nano-photonics,as well as the fundamental test of quantum mechanics in macroscopic system.The minimal model of cavity optomechanics considers the coupling between one optical mode and one mechanical mode.Multimode optomechanics,where two or more optical or mechanical modes are involved,provides an opportunity to reach some regimes where the minimal model is difficult to achieve and to study some more rich and complicated physical phenomena,such as mechanical motion entanglement,energy transfer,and synchronization.The optomechanical systems,due to their inherently engineerable nonlinearities,provide an ideal platform to study self-organized synchronization.Ultrasensitive measurement of a small displacement is an essential goal in various applications of science and technology,ranging from large-scale laser interferometric gravitational wave detectors to micro-electro-mechanical-systems-based force microscopy.The interaction between light in an optical cavity and the motion of a mechanical resonator enables sensitive optical readout of displacement,as well as manipulation of the motion of the resonator through optical forces.The measurable displacement is ultimately limited by the quantum nature of light in a classical optical sensor which is the shot-noise limit(SNL),we can use the bright quantum correlated light to surpass the shot-noise limit of the displacement measurement.The main topics of this thesis are as follows:(1)We demonstrate the self-organized synchronization of phonon lasers in a twomembrane-in-the middle optomechanical system.The probe of each individual membrane enables us to monitor the real-time transient dynamics of synchronization,which reveals that the system enters into the synchronization regime via a torus birth bifurcation line.The phase-locking phenomenon and the transition between in-phase and antiphase regimes are directly observed.The phase difference changes with the optical power after the two membranes are synchronized.Moreover,such a system greatly facilitates the controllable synchronous states,and consequently a phononic memory is realized by tuning the system parameters.Although the effect we have studied is classical,the setup provides a flexible platform for studying quantum collective phenomena and classical-to-quantum transitions.(2)We use the bright quantum correlated light,i.e.,twin beams,generated by a hot rubidium(Rb)vapor cell to surpass the shot-noise limit of the displacement measurement of a membrane in an optical cavity.An improvement of 3 dB in the signalto-noise ratio(SNR)beyond the SNL is realized at an equivalent optical power,by using quantum correlated light with noise squeezed 7 dB below the vacuum level.The sensitivity of 200(?) is achieved.Moreover,the frequency correlation of twin beams is directly measured by using two identical optical cavities,and this relation is utilized to reduce the excess classical noise.This proof-of-principle demonstration should be able to extend to other systems.It also offers a new scheme to study cavity optomechanics,for instance,investigating correlation and entanglement of multiple membranes with quantum correlated light.