Manipulation Of Quantum States In The Cavity Optomechanics System Via Optimal Shortcuts To Adiabaticity

Manipulation of quantum states is the basis of quantum information processing.So far,many effective methods have proposed to manipulate quantum states.Among them,adiabatic technology is currently a widely used and relatively mature technology in the field of quantum information science.The main advantage of adiabatic technology is that it is not sensitive to fluctuations of experimental parameters,and the evolution time does not need to be precisely controlled.However,due to the limitation of adiabatic conditions,manipulation of quantum states via adiabatic passages usually requires relatively long evolution time,which may aggravate the impact of environmental decoherence on the system,and even make the scheme meaningless.To overcome this problem,the shortcuts to adiabaticity are put forward.The technology based on shortcuts to adiabaticity usually makes the system evolve along a non-adiabatic route so that the evolution is accelerated and the final result is the same as that of the traditional adiabatic method.Besides,with the increasing maturity of quantum technology,various different quantum systems are taken as carriers of quantum control theory.Among them,cavity optomechanical systems,which study the interaction between light and mechanical oscillator,not only reveal the physical essence of the transition from quantum physics to classical physics,but also play a crucial role in the fields of high precision measurement,classical signal processing,quantum information processing and so on.In this thesis,we mainly study the manipulation of quantum state in the cavity optomechanical system based on the optimized shortcuts to abiabaticity,such as quantum state transfer among optical fields,microwave fields,and mechanical oscillators,and the preparation of quantum entangled states of mechanical oscillators.The main research results include:1.The quantum state transfer of any two physical systems among optical field,mechanical oscillator,and microwave field is realized based on transitionless quantum driving.With the further development of the theory and experiment of the cavity optomechanical system,electro-optomechanical hybrid system can achieve the conversion between optical signal and microwave signal.We study the model in which the mechanical oscillator couples with both the optical field and the microwave field in a cavity optomechanical system.In order to accelerate the adiabatic evolution,a set of orthogonal normalized base vectors are selected and the expressions of the coupling coefficients are obtained based on transitionless quantum driving.According to the initial and final states of the system,a reversible quantum state transfer between optical field and microwave field is quickly realized by selecting appropriate parameters.By optimizing parameters,the time required to obtain the target state can be minimized.Furthermore,the proposed method is applied to the quantum state transfer between optical field and mechanical oscillator.The effects of the dissipation of cavity and mechanical oscillator on the fidelity of quantum state transfers are numerically analyzed.The numerical simulation results show that,in the case of the given amplitude of optomechanical coupling strengths,the proposed method requires much less evolution time than the adiabatic method,and is more robust against dissipation.2.Quantum state transfer and preparation of maximum entangled state between two mechanical oscillators are realized based on transitionless quantum driving.We apply transitionless quantum driving to study the dynamics of a model in which two mechanical oscillators are set in a cavity.Similarly,appropriate function expressions are selected according to the initial and final states of the system to realize the quantum state transfer and preparation of maximum entangled state between two mechanical oscillators.Further,the parameters are optimized to make the population of intermediate state least or the evolution time shortest.The influence of fluctuations of experimental parameters,dissipations of cavity and mechanical oscillators on the fidelity is analyzed numerically.Numerical simulation results show that the scheme is insensitive to small fluctuations of experimental parameters,and has the strong robustness against dissipation.3.Robust population transfer is achieved based on invariant-based engineering and optimal control.The evolution state and expressions of control fields in the Λ-level system are reversely designed based on Lewis-Riesenfeld invariant.The smooth Rabi frequencies,the systematic error sensitivity,and the population of intermediate state are represented with some auxiliary functions.The research results show that,when the amplitude of control field is given,the population transfer can be realized by optimizing the relevant parameters with the smallest sensitivity of the system error,so as to improve the robustness of the scheme against the system error.Additionally,we apply the idea to achieve robust excitation fluctuation transfer between two membranes in a cavity optomechanical system.The relation between the fidelity of excitation fluctuation transfer and variation of effective optomechanical coupling strengths is numerically analysed.Numerical simulation results show that the drive field expression we selected achieves quantum state transfer with stronger robustness and lower intermediate state population than the existing literature.4.Preparation of maximum entangled state for multi-qubit are quickly implemented with low energy consumption based on path design and optimal control.Firstly,based on the “dark channel”theory,a dark state is designed as the evolution path of the system,and the corresponding coupling coefficients are inversely designed according to the Schr¨odinger equation.According to the initial and final states of the system,selecting appropriate functions can achieve the preparation of the entangled state of -body.There are many types of functions that satisfy boundary conditions,and appropriate functions can be selected to achieve optimization based on the system operating environment.Here,the above theoretical results are used to achieve the preparation of W state of -oscillator in a cavity optomechanics system.The numerical analysis results show that when the peak value of the optomechanical coupling coefficient is fixed,the system evolution time or energy consumption can be minimized by optimizing the parameters.