Study Of The Spontaneous Emission And The Dipole-Dipole Interaction Based On Surface Plasmon

According to quantum electrodynamics,the properties of the spontaneous emission and the dipole-dipole interaction strongly depend on the electromagnetic environment.Surface plasmonic nanostructure is one promising platform to tailor them,since surface plasmon resonance can be generated at the interface between metal and dielectric.Surface plasmons can propagate in structures beyond light diffraction limit and can greatly enhance local electromagnetic field,which are useful in the fields of atom-photon interaction.In this thesis,the effect of surface plasmons on spontaneous emission and dipole-dipole interactions are studied.The details are as follows:Studies show that both the spontaneous emission and the dipole-dipole interaction can be expressed by the classical dyadic Green's function.Therefore,how to accurately and quickly obtain the dyadic Green's function is the key to study the spontaneous emission and the dipole-dipole interaction in artificial nanostructures.In this thesis,a general method is proposed,where the scattered Green tensor is expressed by the difference of the electric fields of an oscillating electric dipole with and without nanostructure around.It can be implemented by using COMSOL Multiphysics software,which is based on finite element method.By this way,the spontaneous emission rate and the energy level shift of a quantum emitter around a nanosphere and a metal-air interface are studied.The results are in good agreement with the analytical ones,which demonstrate the applicability and accuracy of this method.On the other hand,the quasi-static method,which is commonly adopted to obtain the dyadic Green's function,is carefully investigated.It is found that the quasi-static method can be applied more effectively for calculating the energy level shift than the spontaneous emission rate for frequency away from the radiative mode.But for frequency around,there is a blue shift for both and this shift increases with the increasing of emitter-silver distance.Theoretically,the dyadic Green's function is expressed by the sum of a homogeneous part and a scattering part.The real part of the dyadic Green's function is divergent,when the source point and the field point are in the same position.This leads to a divergent level shift.Traditionally,the homogeneous field contribution is absorbed into the definition of transition frequency and it is only need to consider the effect of the scattering part which is non-divergent.Another method is to adopt the renormalization theory.Here,a finite element method for calculating the renormalized Green's function is proposed.Different from the previous scattering Green's function method where two simulations are needed,result can be obtained by simulating only once.It is found that numerical results agree well with the analytical solutions for the homogeneous case,which demonstrates the applicability and accuracy of our method.In addition,the performance of the electric point dipole source and the line current source,which are usually used to obtain the Green function,is investigated.It is shown that the electric point dipole source is more suitable and accurate.The effect of the dipole polarization on the quantum dipole-dipole interaction is investigated when the two atoms are located around an Ag nanosphere.It is found that an atom with linear transition dipole couples much stronger to the other atom with left circularly polarized transition dipole than with right circularly polarized transition dipole.This polarization selectivity phenomena exists over a wide frequency range(0.03eV)and it is robust against variation of the atom's position or the radius of the Ag nanosphere.Besides this stable deterministic coupling,it is also found that the coupling changes suddenly from right circularly polarized to left circularly polarized within a narrow frequency range(0.014eV).For the two dipoles placed along one radial direction of the sphere,an atom with right circularly polarized transition dipole couples to the atom with the same polarization and not to the left circularly polarized transition dipole.Our results should be significant for solid-state quantum-information processing based on the dipole-dipole interaction.