Quantum Dynamical Investigation Of Micro-nano Optomechanical System

Recently years, the coupling between the optical cavity and mechanical system hasbeen focused on one’s attention. Cavity optomechanical system composed of a drivenoptical cavity and a mechanical resonator has also attracted a lot of attention from bothtechnical and scientific communities in physics. Meanwhile, the strong coupling effectin optomechanics cavity, the cooling of the optomechanics and optomechanics inducedtransparency ware demonstrated in succession in the optomechanics system, which pavethe way towards the use of quantum communication and information transfer. In thisthesis, the so-called optomechanics system is the system in which the optical andmechanical degrees of freedom is coupled. We study the quantum optical properties ofthree typical cavity optomechanical dynamics by solving the Heisenberg equation ofmotion, the content and the conclusion are as following.(1) A model describing optomechanical dynamics via radiation-pressure couplingwith a driven optical cavity is investigated by a linearized quantum Langevin equation.We find the spectrum of the oscillator presents normal mode splitting with the increaseof the input laser power in strong coupling regime. The effective mechanical dampingand resonance frequency shift are derived. Furthermore, an approximation scheme wasintroduced to analyze the cooling of the mechanical oscillator. Meanwhile, we givethree key factors which are the bath temperature, input laser power and mechanicalquality factor dominating the ground state cooling. The results that when the bathtemperature is low, the input laser power is high and the mechanical quality factor islarge, the mechanical oscillator can reach its ground state.(2) In Fabry-Perot cavity optomechanical, we start from the Hamiltonian of theoptomechanical system under the condition of detuned to study the quantumphenomenon in the optomechanical cavity. A scattering matrix formulation whichdemonstrates the converting photons to phonons in an efficient and reversible manner isintroduced. This provides a feasible route towards quantum state transfer betweenoptical photons and micromechanical resonators. The phonon-photon transfer maybesuggests a possible quantum optical device. Meanwhile, two methods which arequantum Langevin approximate and a master-equation approach are considered toinvestigate the ground state cooling, and we compare the two methods. Our resultsshowed which scheme is practical under what conditions. The result show that when themechanical quality factor is no so large, the bath temperature is high and laser power isbig, the cooling derived by quantum Langevin approximate is better than amaster-equation approach.(3) The normal mode splitting and ground state cooling in Fabry-Perot opticalcavity and the transmission line resonator optomechanical system is investigated by the linearized quantum Langevin equation, and we compared these two system. The mirrorcan be cooled close to its ground state with low initial temperature and high mechanicalquality factor. Considering the size of the mechanical resonator and precooling thesystem, the mechanical resonator in transmission line resonator system is easier toachieve ground state cooling than in optical cavity.(4) A whispering-gallery modes(WGM) cavity coupling to two parallelwaveguides is devised to study the transmission and reflection of this system. In singlemode WGM cavity, the transmission and re.ection of the optomechanical cavity show"W" and "M" shape mode splitting. Under the action of a controlling and a probe laser,the output field at the probe frequency presents electromagnetically inducedtransparency(EIT)-like spectrum in the system. Our results demonstrate that theresonant interference required for coherent manipulation of light can indeed be achievedvia optomechanical system without the use of atomic resonance.Due to residualscattering of light result in two cavity mode residing in the cavity, the transmission andreflection show three modes splitting. By manipulating the WGM optomechanicalsystem, the system would enable applications for optical processing, where delaying,slowing and storing light pulses could be achieved using the optomechanical devices.This work therefore has broad implications for optical communications and quantuminformation processing.