Entanglement Research Based On Cavity Optomechanical System

Quantum entanglement is the strangest and most mysterious feature of quantum mechanics,which is different from classical physics.It plays an important role in quantum information processing,such as quantum teleportation,quantum cryptography,and quantum computing.In the past,people paid more attention to investigating the properties of quantum entanglement from the microscopic point of view,but often neglected to research quantum entanglement from the macroscopic point of view.The entanglement between macroscopic objects is not only used to verify the basic principles of quantum mechanics,but also an effective tool to study the transition from quantum to classics.Therefore,in recent years,many scientists have begun to study the entanglement between macroscopic objects,hoping to observe quantum properties in a larger physical system.There is an intrinsic coupling mechanism between the optical and mechanical degrees of freedom in the cavity optomechanical system,which provides a good platform for inducing the interaction between macroscopic mechanical resonators and can cause entanglement between mechanical resonators.Previous studies mostly focused on the preparation of entanglement based on the two-mode or three-mode cavity optomechanical system.In this paper,based on the four-mode cavity optomechanical system,the entanglement state between microscopic object and macroscopic object or between macroscopic objects is prepared.We find that the four-mode cavity optomechanical system has different effects from the two-mode or three-mode cavity optomechanical system.It mainly includes the following two aspects work:1.We propose a theoretical scheme to realize the steady-state entanglement between two arbitrary Bose modes in a four-mode cavity optomechanical system including three mechanical oscillator modes and a cavity mode.By using the interaction between the optical cavity mode and the three mechanical modes and modulating the light field to drive cavity mode,we obtain a beam-splitter-like interaction effective Hamiltonian of the system,where the non-localized Bogoliubov modes are cooled and the steady-state entanglement between two arbitrary Bose modes is generated.The influences of oscillator frequency,mechanical damping,and external driving field on steady state entanglement are discussed systematically by numerical simulation.The results show that the proper detuning between mechanical oscillator frequencies is beneficial to enhance the entanglement between two Bose modes.Compared with compression effect,cooling effect plays a dominant role,which is different from the three-mode cavity optomechanical system where compression effect and cooling effect compete with each other.2.A theoretical scheme for the preparation of entangled coherent state of mechanical oscillators is proposed based on the four-mode cavity optomechanical system with two cavities and two mechanical oscillators.By sinusoidal modulation of the tunneling coupling strength between the two cavity modes,the radiation pressure on the oscillators composed of two cavity mirrors is simultaneously increased,and then the displacement of the oscillators induced by single photon is enhanced.By using this mechanism,when the two cavity modes and the two oscillators are initially in the entangled state and the vacuum state,respectively,the whole system evolves into an entangled state under the action of the effective Hamiltonian.The entangled coherent states between oscillators can be obtained by measuring the two cavity states.At the same time,the analytical expression of fidelity between the generated state and the target state is given after considering the actual dissipation of the system,and the experimental feasibility of the scheme is discussed.