Study Of Quantum Simulation And Quantum Coherent Measure Based On Continuous Variables

Over the past 30 years,quantum information,as an important direction,has shown great attraction and developed rapidly.Quantum simulation is an important branch of quantum information science and provides important methods and experiments for the study of quantum information.Although the related work of quantum computation is deepening,the implementation of quantum computation needs to meet high requirements,it is still a difficult problem to directly carry out quantum computation.Compared with quantum computation,quantum simulation has less difficulty relatively,we can use the simpler quantum instruments and experimental platforms to simulate some tasks we feel very difficult at present,research of quantum behavior of systems which makes us to know about some unknown theory,and promote the development of quantum computation and even the quantum mechanics.Continuous variable systems contain many aspects and provides a wide range of carriers for quantum simulation.Therefore,the study of quantum information and sim ulation of continuous variable systems is getting more and more attention.As an important platform,ion trap shows great potential in realization of entanglement of discrete ions,cooling and studying phonon dynamics.In 2009,L.M.Duan etal proposed to add the non-hannonic potential in the axial direction of the ion trap to achieve the equidistant of ions,meanwhile,he theorized that this ion trap can trap an infinite number of ions which makes ion trap to be the excellent candidate for quantum computation and simulation.In this paper,combining with the ion trap which is an important instrument,we propose a scheme to realize Anderson localization and analyze the properties of this model by numerical simulation,so as to provide a theoretical method for effectively preventing thennalization in ion trap.The optomechanics system combines the optical mode and mechanical mode to achieve some specific functions,such as we can realize the precise measurement of parameters of the system through the output light,carry out diodes and triodes and so on.In the optomechanics system,we propose a method to realize the optical diode and triode.Compared with the previous method,theoretically speaking,the triode we simulated has obvious advantages in the aspect of magnification,and the external force can be accurately measured according to the magnification of the triode.The non-Markovian environment can preserve the quantum coherence which is an important physical resource.The related work that we have done will have a positive effect on the study of quantum information of continuous variable systems.Here's an overview of our work:1.The existence of disorder and quasi-periodic characteristics will lead to a famous phenomenon--Anderson localization.Here,we have used the non-uniform Bessel laser standing wave to introduce the quasi-periodic characteristics into the ion trap system,so as to achieve localization of the phonons in the ion chain.Considering that the coulomb forces between ions are long-range interactions,so the tunneling happens between any two ions,the localization phenomenon of our model is more complex than that of AA model.The study of this problem not only helps to further understand the phenomenon of Anderson localization,but also provides a theoretical simulation for preventing the thermalization in ion trap.2.Based on the Anderson localization model realized in ion trap,we conduct a deeper study on its phase transition and critical values,and give an approximate mobility edge.By studying the influence of the horizontal frequency of the trap ion on the eigenfunction of the single particle state,we found that when the transverse imprisoned frequency is bigger,the eigenfunctions and the their critical values are not sensitive to transverse frequency,even critical values of eigenfunctions are independent of the transverse frequency if the transverse one is much larger than effective strength of the laser.The characteristics reveal that the threshold which is given by a certain transverse frequency has general usability for others,if the transverse frequency is large enough.That improving the transverse frequency is certainly beneficial to the improvement of the stability of systems and the number of ion,which is advantageous to the quantum simulation.3.In the optomechanics system,we realize the non-reciprocity of the system by introducing external forces and the controlling light field to destroy the symmetry of the system.In fact,the external force and the controlling light field can adjust the system in the rotating wave and the anti-rotating wave states.Under the condition of rotating wave,the cavity mode which interacts with the controlling light field shows the phenomenon of optomechanically induced transparency at a certain frequency,and the detected light field is rarely absorbed.The another cavity mode(which has no interaction with the controlling light field)is fully absorbed at this frequency,and a diode is achieved.The detected field interacting with the controlling light field is amplified under the condition of ant-rotating wave process.In this work,we also analyzed the relationship between ampl ification rate and parameters of our system,provided theoretical simulation for regulating and controlling triode,and proposed a method of measuring external force and other parameters by output light field.4.Study the dynamic behavior of quantum coherence measure in non-Markovian environment.We give the evolution dynamics of quantum states through the master equation under the non-Markovian environment,and then obtain the mathematical form of the quantum coherence varying with time,and analyze the influence of parameters of the system on the quantum coherence.We find that when the coupling strength between the environment and the system is greater than the critical value,the quantum coherence of the system will be frozen to a non-zero constant,which is determined by the initial state of the system and the environment.Otherwise,th e quantum coherence of the system will be dissipated in the case of the environment is the thermal bath.This provides a theoretical reference for the regulation of quantum coherence.