Compressive Cooling Of Micromechanical Vibrator In Cavity Optomechanical System

The field of cavity optomechanics takes advantage of the parametric coupling between cavity optical field and mechanical oscillator mode to study the interaction between light and matter.Specially,cavity optomechanics utilizes electromagnetic field such as optics and microwave to measure and control the mechanical motion,especially mechanical oscillator in quantum realm.For the purpose of precise control on mechanical mode,the pivotal step is to cool the mechanical resonator down to quantum ground state as far as possible,that is,with an average phonon occupation below one quanta.But,the combined system of optical field and mechanical oscillator is inevitably with the coupling to individual environment.And the occurrence of system quantum noise imposes a very strong limitation,that is quantum backation limit,which limits the minimum temperature being approached by conventional laser cooling technique.The first part of the paper mainly introduces the basic research in the field of cavity optomechanical system,the research progress of the cooling researching of micromechanical oscillators in the cavity optomechanical system and the basic theoretical methods needed to deal with such an open system;The scheme for realizing the cooling of the vibrator includes a brief summary of the active feedback cooling technology and the self-cooling technology of the mechanical oscillators.In the self-cooling technology of micromechanical oscillator,the basic theory of the most widely studied resolved sideband cooling technology is analyzed in detail in this paper.To break through the achievable minimum temperature by conventional laser cooling technique,in the later part of this paper as also our main research work,we propose the squeezed cooling scheme in this paper.Resorting to the quantum squeezing effect induced by the parametric amplification,the fluctuation of one quadrature of the parametric oscillator is reduced below standard quantum limitation while the fluctuation of the other conjugate quadrature is amplified.Then,the cooling process can be heavily facilitated if the light mode directly couples to the "heated" quadrature and the "hotter"phonons are taken away quickly by the leakage photons from the bad cavity,which can deeper cool the mechanical oscillator.Based on this theoretical idea,firstly,we give the Hamiltonian of the whole system,especially the part of Hamiltonian inducing the quantum squeezing of the mechanical oscillator.We analyze the classical and quantum dynamics of the driven parametric mechanical oscillator under the effect of the optical field.Then,taking advantage of the fundamental approach to solve the open systems,we deduce the quantum Langevin equations including the noise from the system environments.Further,from the dynamical equations given,we demonstrates analytically and theoretically that the increasing squeezing factor can effectively decrease the phonon number spectra curves,which illustrates that the "heat" phonons of the oscillator can be further extracted via squeezing on motion of mechanical oscillator to reduce the effective temperature of mechanical mode below quantum shot noise.This method can quickly achieve cooling mechanical oscillator to quantum ground state below standard quantum limitation.