| The field of cavity optomechanics discuss the interaction between optical field(Microwave field)and nano-mechanical or micro-mechanical motion.Now many experiments in this field like optical measurements of mechanical motion,dynamical back action amplification and cooling of mechanical motion,nonlinear dynamics,multi-mode optomechanics exhibit that their mutual optomechanical interaction mediated by the radiation-pressure force.It is a proposal for future experiments about cavity photo-mechanics.There are many special advantages in cavity optomechanical system,such as the small size of the volume of optical mode,the high quality factor,and the high quality factor of micro-mechanical motion.And with the development of modern technology,the advantages of the cavity optomechanics become more and more prominent,which make the accuracy and operational level to improve a lot.This is attracting more and more scholars greatly to study the cavity optomechanical system.At present,cavity optomechanics has already become one of very important research systems.The research is carried out mainly based on the high quality and micron even to nanometer level of volume to significantly enhance the interaction between cavity mode and oscillator,then to realize the coherent control of optics and mechanical movement.For example,to preparation the entanglement state between optics and vibrator,vibrator and vibrator,optics and optics and so on.At present,cavity optomechanical systems with micro-mechanical membrane have get wide attention,in which optical and mechanical degrees of freedom are coupled through radiation pressure.These cavity optomechanical systems provide us a promising future about exploring the boundary between quantum and classical mechanics and controlling the quantum states of light and m atter.Theoretical proposals suggest that an optomechanical device can be able to generate squeezed light,entangled optical and the superposition states of mechanical oscillators and quantum non-demolition measurements of a mechanical oscillator's system when the device is consisted of one optical cavity which detuned by the motion of a micro-mechanical oscillator.But achieving these goals requires a optical cavity with high finesse and micro-mechanical oscillators with high quality factor.High mechanical quality factor is asked for reducing the coupling of oscillator to the environment,and high optical finesse is required that it can increase the optomechanical coupling for each incident photon.However,a cavity photo-mechanical system is difficult to possess both mirrors with high finesse and micro-mechanical resonator with high quality factor.Through research,scientists have finally found a kind of material that is silicon nitride membrane,as a micro-mechanical oscillator whose frequency changes in a large range and it is easy to integrate with other quantum systems,such as the quantum dot in optical cavity and microwave cavity.Mechanical membranes have a high quality factor and do not significantly reduce the accuracy of cavity photo-mechanical system.The commerce of silicon nitride membrane center on low-stress membranes.It is transparent to visible light,X-rays and electrons.Because of this characteristics as well as suitable size,smooth surface,chemical inertness and so on,they have significant strength against static loads.In addition to,they also possess dynamic mechanical properties,near-infrared optical properties.In this paper,we have researched the interaction between light and the micro-force in cavity optomechanical system with three silicon nitride membranes and the preparation of entangled state on mechanical mode.In the first part of this paper,we use a cavity optomechanical systems which has three micro-mechanical membranes.The whole length of the optical cavity is 4L,three micro-mechanical membranes are oscillated near-L,0,L,and we use the method of transfer matrix to change turbid medium with three membranes into turbid medium with one membrane equivalently,according to the model of the turbid medium with many membranes.Then we calculate the reflection and transmission of the equivalent single mode,and the dispersion relation of the system when the system reaches the condition of resonance transmission and the maximum transmittance.Then,based on the expression of the solution,we have studied deeply on the dispersion relation of the system.In the first step,the numerical solution of the expression has been solved at the balanced position and plotted.It is found that the reflection and transmission of the three mechanical membranes resulted in that the eigen mode of the system splitting into a set of four modes.And preducing avoid cross-effects due to the coupling between sub-modes.In the second step,we calculated the four eigen modes of the system at balanced position without considering the motion of the mechanical oscillator.Then,using the perturbation theory,we analyzed respectively from the coupling of the cavity mode and the center of mass motion mode to the coupling of the cavity mode and the relative motion mode.We can conclude that the four eigen modes can be coupled with the convergent movements Q secondly at the balanced position Q0 and q0 of the mechanical oscillator.And coupled with the cavity field lineally and secondly by driving different intrinsic modes.It is,of course,also possible to manipulate the interaction between the optical mode and the mechanical mode by adjusting the balanced position of the mechanical membranes.In the second part of this paper,we discuss the preparation of entanglement in a cavity optomechanical system with two membranes.As a core resource for quantum information,quantum entangled state has a very important value in the field of quantum information,such as to inject an entangle light to achieve entanglement,to achieve entanglement between mechanical oscillators through optics to regulate the non-degenerate parametric interaction.In addition,the entanglement can also be obtained by linear mixing position and momentum of compression source.In this paper,we discuss the use of mechanical oscillator within the Duffing non-linear characteristics to achieve compression of mechanical vibration.Then,under the condition of weakly coupled approximation of cavity mode and mechanical vibration mode,to achieve the the linearly mixed interaction between the oscillator.This will produce entanglement between mechanical oscillators,then analyze the entanglement between the mechanical vibrators according to the judgment criteria of two-mode Gaussian entangled state. |
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