Quantum Simulation Of A Three-mode Optomechanical System Based On The Fredkin-type Interaction

The field of cavity optomechanics foucus on the studies of the radiation pressure interaction between optical field and the mechanical oscillator,and the physical effects induced by the optomechanical interactions.Cavity optomechanical systems have important applications in quantum precision measurement,quantum information and quantum computing.The applications include gravitational wave detection,preparation of non-classical states,optomehcnical-induced transparency,and preparation of single-photon sources.With the development of this field,many interesting physical effects and physical phenomena caused by optomechanical interactions have been experimentally confirmed.People use this system to control the quantum properties of macroscopic objects,explore the boundary between quantum and classical,and demonstrate the fundamental problems in quantum mechanics.In 2017,the Nobel Prize in Physics was awarded to three scientists work on gravitational wave detection.The experimental platform they designed has some relating features with the optomechanical systems.Therefore,as a physical platform,the optomechanical mechanical systems have research significance.The realization of multimode optomechanical interactions in the singlephoton strong-coupling regime is an important research goal in cavity optomechanics,but it remains a challenge in practical physical systems.We propose a reliable scheme to implement quantum simulation of a three-mode optomechanical model based on the Fredkin-type interaction.In particular,we consider a Fredkin-type interaction model,which consists of three bosonic modes,here the three bosonic modes play the role of an optical mode(the conditional controller mode in the Fredkin interaction)and two mechanicallike modes(the two modes involving the exchange coupling).By introducing strong drivings to the two mechanical-like modes,in the displacement representation,this will lead to a three-mode optomechanical interaction with two enhanced coupling strengths.As an application of this enhanced threemode nonlinear optomechanical coupling model,we show how to generate entangled-cat states of the mechanical-like modes using the conditional displacement mechanism.The quantum coherence and entanglement effects in the generated states are investigated by calculating two-mode joint Wigner function and quantum entanglement.The influence of the dissipations on the state generation is considered in the open-system case.This work will open a route to the study of ultrastrong multimode optomechanics.This thesis consists of five chapters:In the first chapter,the research background and significance of cavity optomechanical system are introduced.In the second chapter,the background knowledge of this thesis is introduced,including two-mode cavity optomechanical systems,multi-mode cavity optomechanical systems,entangled coherent states,the Fredkin-type interaction,logarithmic negativity and so on.In the third chapter,we introduce the Fredkin-type interaction model.By applying suitable driving to the system,a three-mode cavity optomechanical system is simulated under suitable parameter conditions.We also study the preparation of entangled cat states based on the three-mode cavity optomechanical system.By calculating the two-mode joint Wigner function and the logarithmic negativity,we show the quantum coherence effect in two mechanical-like modes.In the fourth chapter,we consider the interaction between the system and the environment,and we use the master equation method to study the influence of quantum dissipations on the state generation in the open-system case.In the fifth chapter,we present a summary and outlook for this paper.