Research On The Casimir Effect In Different Systems

The Casimir effect is the interaction between two objects that are located at a distance of micro and nanometers.It is a macroscopic quantum phenomenon originating from the zero-point energy change of the electromagnetic field around material boundaries.This effect can be subdivided into the static Casimir effect,the dynamical Casimir effect,and the Casimir-Polder force.The dynamical Casimir effect is a phenomenon in which the virtual quantum fluctuations in the system are transformed into real photon pairs due to the change of the boundary conditions of the quantum field in the vacuum.The photon pair exhibits quantum characteristics such as quantum discord,quantum entanglement,and quantum steering in experiments,so the dynamical Casimir effect is considered as an important resource quantum technologies,such as quantum metrology and quantum cryptography.The Casimir-Polder force is a long-range interaction between a neutral polarizable particle and an object.Affected by the initial state of the atom,the material properties of the conductor plate,the medium,etc.,the Casimir-Polder force can be either attractive or repulsive.Therefore,the research and application of Casimir-Polder force in micromechanical systems has been widely concerned.In this paper,we study the disruptive evolution of quantum correlation in the dynamical Casimir effect,and the dynamical Casimir-Polder force between a two-level atom with different initial states and a one-dimensional output coupling cavity with dielectrics.The research content is as follows:In the first part,we study the quantum entanglement and Gaussian interference power in the dynamical Casimir effect in the thermal reservoir environment with the temperature of 4K based on the superconducting circuit experimental device that generates the dynamical Casimir effect.Firstly,the specific expression of the dissipative evolution of dynamical Casimir effect is derived through the master equation of dissipation evolution,and the concrete form of the Peres-Horodecki Separability(PHS)criterion and Gaussian interference power are obtained according to this expression.Then the PHS criterion is used to determine whether the state of the system is entanglement state under different conditions,and the effects of various parameters on entanglement are analyzed.Finally,the non-classical characteristics of the system under different parameters are analyzed by using Gaussian interference power.By comparing them,we find that entanglement is very fragile to dissipate,while dissipation has a relatively weak influence on Gaussian interference power.In the second part,based on the above work,we study the Einstein-Podolsky-Rosen(EPR)steering and the teleportation fidelity in the dynamical Casimir effect in a thermal equilibrium environment.During the research,two environments are considered,one is the sample environment that produces the dynamical Casimir effect,and the other is the transmission line coupled with the sample environment,that is,the thermal reservoir environment.Under the condition that the temperature of the thermal reservoir environment is the same as that of the sample environment,we discuss the effects of temperature,detuning,driving amplitude,and damping on decoherence.The results show that the loss of the EPR steering and the teleportation fidelity is slow at low temperature,the driving amplitude has no effect on EPR steering,and the detuning and asymmetrical damping have great impact on EPR directional steering.Under the condition that the temperature of the thermal reservoir is much higher than that of the sample,we find that the sensitivity of the EPR steering and the teleportation to different degrees of the asymmetric thermal noise is different.Therefore,it is very important to choose a suitable asymmetric noise channel to protect the EPR directional steering.In addition,through the comparison between the EPR steering and the teleportation fidelity,we have obtained a directional steering that is more suitable for quantum teleportation in this system,and found that two-way steerable are always suitable for quantum teleportation.In the third part,we study the dynamical Casimir-Polder force between a two-level atom with different initial states and a one-dimensional output coupling cavity(dielectric cavity)with dielectrics.We use the perturbation theory to calculate the analytical expression of the dynamical energy shift between the superposition atom and the dielectric cavity.Based on this,firstly,we obtain the dynamical Casimir-Polder force between the ground-and excitedatom and the dielectric cavity,and compare them through numerical analysis.The results show that before the round-trip time,The Casimir-Polder forces of the ground-and excitedatom in the dielectric cavity are equal and opposite in nature(attractive or repulsive),and after the round-trip time,the intensity of the dynamical force for the excited atom exceeds that for the initially bare ground state by about three orders of magnitude.In addition,the Casimir-Polder force of the excited atom oscillates with its position,and there are multiple equilibrium positions where the Casimir-Polder force is zero in the cavity.Then we obtain the time-dependent expressions of the interaction force between the atom in different initial states and the dielectric cavity,discuss the relationship between the interaction force and atomic positions,and the effects of the relative dielectric constant and atomic transition frequency on the equilibrium positions,and analyze the relationship between interaction forces and atomic initial states.The results show that the relationship between the superposition atom and its position is similar to that of the excited atom,and the equilibrium position is mainly affected by the relative dielectric constant and atomic transition frequency.In addition,by selecting the appropriate initial state,the interaction force between the atom and the dielectric cavity can also be zero.Therefore,we can control or eliminate the influence of the Casimir-Polder force in experiments and devices by changing the atomic position,dielectric,atomic transition frequency,and atomic initial state.