The Classical And Quantum Dynamics And Application Of Optically Levitated Nano-particle

Because of the improvement of micro-and nano-fabrication,optomechanics as a preci-sion measurement tool and experimental platform has attracted more and more attentions.This system is widely used in high-precision measurement,preparation of macroscopic quantum state and quantum ground state cooling.Optically levitated nanoparticle system is a novel optomechanical system and has high quality factor and reconfiguration.Based on these property,this system has been used to research some important topics,including the measurement of instantaneous velocity of Brownian particle,the proof of fundamental laws of thermodynamics and etc..Based on the optically levitated nanopartilce system,this thesis will study the precision measurement and quantum state cooling by utilising the high quality factor and reconfiguration of this system.By utilizing optically levitated nano-particle system and the most advanced detective technology,the instantaneous velocity of Brownian particle has been measured.Inspired by these investigations,we have proposed a detection scheme for magnetic field gradient and single spin.We theoretically analyzed the ratio between the fluctuation of particle’s displacement caused by spins in magnetic field and caused by molecular collisions of the residual air.When the ratio is larger than unity,the displacement fluctuation of spins flipping can be remarkably detected.By theoretical analysis and numerical simulation,we propose and validate a scheme for the detection of gradient of the magnetic field by levitating ferromagnetic nano-particle,and also put forward a realizable detection scheme of the single spin by levitating nano-diamond particle with single nitrogen-vacancy(NV)centers.In general case,the optically levitated particle is simplified as a sphere,however,irreg-ular shape is more common.The reports about the librational mode and translational mode of optically levitated ellipsoidal particle have provided experimental base for investigation of librational mode of particle.We systematically investigate the bistable behaviour and squeezing property of the librational mode of a levitated nonshperical nanoparticle trapped by laser beams.By expanding the librational potential to the forth order of the librational angle θ,we find that the nonlinear coefficient of this mode is only dependent on the size and material of nanoparticle,but independent of trapping potential shape.The bistability and hysteresis are displayed when the driving frequency is red-detuned to the librational mode.In the blue-detuned region,we have studied squeezing of the variance of librational mode in detail,which has potential application for measurement of angle and angular momentum.Optically levitated ellipsoidal particle not only have librational mode,but also have translational mode.The coupling between librational mode and translational mode must be considered in some research topics.Based on this property,we systematically investigate the multistability behaviour and sympathetic cooling of the librational mode and translational mode of a levitated nonspherical nanoparticle trapped by laser beams.By expanding the trapping potential about translational and librational freedom degree,we deduce the nonlinearity of the librational mode and translational mode and their coupling.By stability analysis,we find that the system will presents multistability when any driving frequency is red-detuned.The system will single stable state if and only if these two driving frequency are blue-detuned at the same time.In the single stable region,we have studied the cooling scheme of translational mode utilising librational mode,and found that matching driving amplitude of these two mode and suitable vacuum degree can realise sympathetic cooling.Combining feedback cooling,the sympathetic cooling efficiency have been improved.