The Dynamical Behavior Of Cavity Optomechanical System

With the widely application and development of the mechanical system and optical microcavity, the strong coupling between mirror and cavity field in the system of cavity optomechanics,that make the optomechanical system become an important platform which is used to inspect macroscopic quantum phenomena and text quantum theory, so that become a new research hot spot. At the same time, for cavity opto-mechanics, there are important application prospect in gravitational waves detection, infinitesimal displacement and the precision measurement of the quality and so on, therefore the study of cavity opto-mechanics has the profound significance. In this paper, we study the dynamics behavior characteristics of the cavity opto-mechanical system, and investigates the influence of the end mirror vibration to the atomic emission spectrum of a single two-level atomic in the cavity.About the dynamical behavior of the cavity optomechanical system, we first investigated the two-level atomic occupancy, found only when the initial state of cavity field the mirror are in Fock state, and that the initial state of the atomic is excited state (or ground state), the evolution curve of the atomic occupancy is cosine curve, and it’s frequency is2ηn(m5+1). The atomic occupancy’s evolution with the time is very sensitive to the motion state of the mirror, if the oscillator’s initial state is in the coherent state,<S2(t)> will present collapse and reply phenomenon, collapse time depends on the<n> of the cavity field and<m> of the oscillator, reply time related to<m>.About the coherence of the light field of cavity optomechanics, we mainly studied the second order degree of the light field. We obtained that it is mainly determined by the initial state of light field, at the same time it will be affected by atomic initial state and oscillator’s. Compared with the J-C model, that when light field in Fock state, the second order degree of light field present a periodic oscillation that depends on<n>. In the cavity optomechanical system, because of the vibration of the mirror, even if the light field in Fock state, the collapse and reply also happens, with the increase of<m> the collapse of the first time, and the recovery time depends on<m>, and only when light in coherent state or its add photo number far less than<n>,the light field will appear the bunching effect.We also study the laws of the evolution over time of the linear entropy of the atom and light field of the cavity optomechanical system. We found that, when the light field and oscillator are in Fock state, the evolution curve of their linear entropy are cosine oscillation curve between0and0.5. Because of the mirror vibration state, even if the light field in Fock state, they also can appear the periodic collapse and reply, and this moment Sa(t) is equal to Sf(t).In this paper, we study the atomic emission spectrum of a single two-level atomic in the cavity, and analyze the influence of the vibration of mirror for it. We found that the average photon number of cavity is equal to the average possession number of oscillator the atomic emission spectrum will present a single wave at the transition frequency, but if they are not equal symmetrical bimodal will appear. When the light field and the oscillator in Fock state there will appear the peaks symmetrical on both sides of spectrum line, with the increase of the coefficient of the cavity field or the oscillator, the symmetrical edge peaks will turn into the symmetrical wave group.