Study Of Casimir Effect In Low Dimensional Micro Cavities

Generally speaking,the vacuum energy tends to be infinite,and cannot be observed directly.However,the Casimir effect,which is the zero energy fluctuation of the electromagnetic field,is becoming one of the best witnesses of the observed quantum effect.H.B.G.Casimir firstly predicted that two parallel conductive plates in the vacuum environment will attract each other,and it was then named as Casimir effect and is observed soon successfully in experiments.As the development of the technology,the measurement in the experiment is also becoming more and more accuracy.Not only the attractive force,but also the repulsive force was furthermore observed in 2009.Moreover,Wilson found the dynamical Casimir effect,which generates real photons when the boundaries of the electromagnetic field moves fast.Actually,and it is consistence with the theoretical prediction about the dynamical Casimir effect in 1970 by Moore..Nowadays,the Casimir effect has been widely used in mathematical physics,atom and molecule physics,condensed matter physics,biology as well as astrophysics and cosmology and is of great application in the field nano-technology.Motivated by its importance,we study the Casimir effect in different type micro cavities in this thesis.First of all,we study the stationary Casimir effect in 1D microwave laser cavity utilizing a full quantum theory.By use of Fox-Li quasimode theory,we calculate the Casimir energy and give the analytical expressions between two cavity walls and discuss the exotic property of the Casimir force.Furthermore,we discuss the effect of length of the cavity and the decay rate on the Casimir effect and compare the results to the ideal case.Secondly,we study the collective excitation effect when an ensemble of atoms are put into a resonant non-stationary cavity and the Casimir effect.As the first step,we give the Hamiltonian of the system based on the excitation model of the atomic ensemble.Then,according to the equation that the density matrix satisfies,we obtain the average photon number and excitation number generated by the dynamical Casimir effect,when the cavity is prepared in the thermal state initially.Also,with the assistance the numerical simulation,we give their curves as functions of the evolution time,and demonstrate the effect of the temperature,coupling strength to the dynamical Casimir effect and the collective excitation effect of the excitons.At last,we subsequently discuss the case when the cavity is prepared in the squeezed vacuum state initially and give the effect of the squeezed parameters and the coupling strength.Therefore,we will build the foundation for the study of Casimir effect in complex cavities.