Study On Ground State Cooling And Phonon Blockade Of Mechanical Oscillator In A Quadratic Optomechanical Coupled System

Cavity optomechanics as a crucial branch of physics which focuses on the interac-tion of controllable radiation pressure between light and mechanical motion has aroused wide interest in recent years.With the continuous development of nano manufacturing technology in materials and technology,nano scale mechanical oscillator has become a key research object,which provides a advantageous research platform for the study of quantum manipulation of macro mechanical system.The cavity optomechanical system composed of nano mechanical oscillator and optical cavity has important applications in high-precision measurement of displacement and mass,quantum information process-ing,and exploring interesting physical phenomena under the quantum-classical boundary.Although the mechanical oscillator is very sensitive to deformation,its precision mea-surement is still limited by thermal noise.In order to further improve the measurement sensitivity,it is necessary to eliminate thermal noise and cool the mechanical oscillator to its quantum ground-state.The ground-state cooling of the mechanical oscillator is the primary problem to be solved in optomechanics.Many schemes have been put for-ward around this issue,such as sideband cooling,dissipative cooling,the most common research method is sideband cooling.According to the decay rate of the optical cavity less or greater than the mechanical frequency,sideband cooling can be divided into two categories:resolved sideband cooling and unresolved sideband cooling.Due to the high requirements for the high quality factor of optical cavity,it is difficult to realize ground-state cooling in the resolved sideband limit in most physical systems.Therefore,it is very important to realize ground-state cooling in an optical cavity with low quality factor.On the other hand,phonon blockade has attracted extensive attention in recent years due to the need of preparing single phonon sources.In this paper,we study the ground-state cooling scheme of the mechanical oscillator under the unresolved sideband mechanism in the quadratic optomechanical coupling system,and propose a feasible scheme of the phonon blockade.The contents of this paper are arranged as follows:Firstly,the ground-state cooling scheme is proposed for the quadratic optomechanical coupled system including double cavities.In this scheme,the coupling between the optical cavity and the mechanical oscillator is directly proportional to the square of the position of the mechanical oscillator.By introducing an auxiliary optical cavity,a quantum interference mechanism is established in the system.The results show that due to the introduction of an auxiliary cavity in the optomechanical system,a quantum interference effect is produced,the Lorentz spectrum of a single cavity optomechanical system is split into two narrow peaks and a lower dip like electromagnetically induced transparent(EIT)spectrum.The appearance of dip means that the heating effect is suppressed,while the two peaks represent that the cooling effect is enhanced.Compared to the linear optomechanical coupling,a faster cooling rate is achieved in the current scheme due to the two-phonon absorption.By deducing the optimal parameter conditions,the ground-state cooling of the mechanical oscillator with a high efficiency can be achieved even in the unresolved sideband mechanism and weak coupling.Secondly,the phonon blockade effect is studied in a the hybrid optomechanical system including a two-level quantum emitter.By decoupling the cavity modes,the system can be simplified as a two mode interaction,i.e.,the linear coupling between the quantum emitter and the mechanical oscillator,and a weak Kerr nonlinear effect is generated.Under the condition of weak driving and weak coupling,the statistical characteristics of phonons exhibit antibunching effect,due to the quantum interference between two different paths.By deriving and analyzing the analytic solution of the second-order correlation function,the optimal parameter conditions for ideal phonon blockade effect can be obtained.The results show that the strong phonon blockade effect can be produced even under the condition of weak optomechanical coupling.