Ground-state Cooling Of The Mechanical Oscillator And Preparation Of Nonclassical States In Cavity Optomechanical Systems

Broadly speaking, quantum optomechanics provides a universal tool to achieve the quan-tum control of mechanical motion. With the advancement of fabrication technology, it does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from10-20g to several kilos. At a fundamental level, it offers a route to determine and control the quantum state of truly macroscopic objects and paves the way to experiments that may lead to a more profound understanding of quantum mechanics; and from the point of view of applications, quantum optomechanical techniques in both the optical and microwave regimes will provide motion and force detection near the fundament limit imposed by quantum mechanics. Optomechanical quantum control requires the mechanical oscillator to be in or near its quantum ground state. Moreover, optomechanical squeezing is not only a fun-damental feature of quantum character of macroscopic objects but also critical for surpassing standard quantum limits on position and force sensing, and for constructing the next generation of gravitational-wave observatories. Therefore, nowadays the investigations of optomechanical cooling and squeezing of mechanical oscillators become a research focus.Our research motivations are mainly based on how to find the methods to improve the mechanical cooling performance and achieve better squeezing of mechanical motion. We first propose a fast ground-state optomechanical cooling scheme compared with the widely imple-mented resolved-sideband regime, where the cooling process is limited by small damping rate of the cavity field and small driving strength with respect to the detuning. Our model is con-sisted of a two-mode optical cavity with a quarter-wave plate inside. Two cavity modes are orthogonally polarized, and one cavity mode dissipates to the external environment at a fast rate while the other dissipates at a slow rate. The quarter-wave plate provides linear mixing interaction between these two cavity modes. We adiabatically eliminate the cavity variables in the weak coupling limit and find that the cooling process for the oscillator is dominated by scattering process via the fast-decay channel, which is significantly enhanced as compared with that obtained in the resolved-sideband optomechanical cooling scheme. Meanwhile, the heating process is significantly suppressed by exploiting the destructive quantum interference between the two cavity modes with the help of the quarter-wave plate.Recently a new type of optomechanics:dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode, is theoret-ically proposed and experimentally investigated in microwave domain. An effective dissipation optomechanics in optical domain has already theoretically investigated to achieve the ground s- tate cooling of oscillator via utilizing the completely destructive interference of quantum noise. We investigate the generation of squeezed states in a movable mirror in dissipation optome-chanics. Via feeding broadband squeezed-vacuum light accompanying a coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory. When the mirror is weakly coupled to the cavity mode, we find that the driven cavity field can effectively perform as a squeezed-vacuum reservoir for the movable mirror via utilizing the completely destructive interference of quantum noise. Efficient trans-fer of squeezing from the light to the movable mirror occurs, irrespective of the ratio between the cavity damping rate and the mechanical frequency. Moreover, when themirror is moder-ately coupled to the cavity mode, photonic excitation can preclude the completely destructive interference of quantum noise. As a consequence, the mirror deviates from the ideal squeezed state.Alternatively we investigate another method to generate the squeezed state of the mirror motion in a dissipative optomechanical system via driving the optical resonator with a strong laser field accompanied with two periodically-modulated lights. We also proceed the lineariza-tion method on the quantum dynamics to analyze the squeezing of oscillator motion, i.e., as-suming that each operator in the system can be written as the sum of its mean value and a small fluctuation. Using the density operator approach we calculate the variances of quantum fluctu-ations around the classical orbits, and then analyze the quantum behavior of the system around the classical value. Both the numerical and analytical results predict that the squeezed state of the mirror motion around its ground state is achievable. Moreover, the obtained squeezed state is robust against the thermal noise because of the strong cooling effect outside the resolved-sideband regime, which arises from the destructive interference of quantum noise.At last we summerize our research contents and present some outlooks on the research topic.