Optomechanically Induced Transparency In The Quadratically Coupled Optomechanical System

An optomechanical system(OMS)describes the optomechanical interaction between the movable mirror and the cavity optical field induced by the radiation pressure.It has attracted much attention because of its potential applications,such as in entangling the macroscopic oscillator and the cavity field,cooling the mechanical vibrations to their quantum ground states,generating the macroscopic quantum superposition and demonstrating the optomechanically induced transparency(OMIT).In this thesis,our main task is to investigate the OMIT in the optomechanical cavity with the quadratic coupling.We propose the schemes of the parametrical driving on the mechanical oscillator and investigate its effects on the OMIT.And,the OMIT for probe field propagating through the double quadratically coupled optomechanical cavities within a common reservoir has been considered.Subsequently,we investigate the OMIT for the finite-bandwidth squeezed field in the optomechanical cavity.The results are summarized as follows:1?Firstly,we present a scheme of a mechanical manipulation of the probe absorption properties in a quadratically coupled optomechanical system in which the nanoresonator is parametrically driven by a time-dependent potential.It is found that by tuning the mechanical parameter the two-phonon optomechanically induced transparency can be enhanced and the perfect transparency arises.Here,the transparency frequency(the probe frequency for the maximal transparency)is not shifted when the transparency is improved by using the mechanical driving.This overcomes the shift of transparency frequency in the scheme of the enhanced transparency by using a coupling field.In particular,the probe amplification occurs by tuning the mechanical parameter,which is an optical evidence for the mechanical parametric amplification based on the optomechanical platform.In the amplification region,the amplification is enhanced by increasing the mechanical driving parameter or by decreasing the power of the coupling field.These investigations will be useful for the squeezing or in producing a low-power and high-amplification parametric amplifier for optical fluctuations.2 ? Then,we investigate the OMIT for a finite-bandwidth squeezed field propagating through the quadratically coupled optomechanica system.The result shows that the OMIT dip for the squeezed field becomes much deeper and wider with the coupling field,and the transparency position is shifted to higher-frequency.Additionally,we have found that the photon number for the squeezed field can improve the OMIT.Also,it is found that the transparency is markedly dependent on the bandwidth.Finally,it is shown that the temperature of the environment can improve the transparency in the quadratically coupled optomechanical cavity.Our results provide a possible scheme for enhancing the cooling of the membrane.3?Finally,we consider the optomechanically induced transparency in the double quadratically coupled optomechanical cavities within a common reservoir,in which the two cavities are driven by the coupling fields.It is shown that the probe transparency is improved by increasing the coupling field(the left coupling field)applied on the probing cavity,but the transparency position(the probe frequency of the maximal transparency)is shifted to high frequency.The coupling field(the right coupling field)applied on the other quadratically coupled cavity can lead to a low-frequency shift for the transparency position,which can be used to fix the transparency position by adjusting the right coupling field.We get the quantitative findings that the transparency position is exactly determined by the intensity difference between the two coupling fields.On the other hand,it is found that when the two coupled optomechanical cavities interact with their common reservoir,the cross decay induced by the common reservoir can improve the probe transparency and widen the transparency window.Finally,the effects of the environment's temperature on the transparency are investigated.This will be useful in cooling the membrane,squeezing and entangling the output fields.