Decay Dynamics Of A Two-level Atom In Surface Plasmonic Nanostructure

Decay dynamics of an excited atom lies at the heart of quantum optics,and can be widely applied in the fields of quantum computation and quantum state manipulation.Due to the strong field enhancement,surface plasmon can greatly enhance the light-atom interaction and can greatly modify the decay dynamics.In this thesis,we investigate the effect of the surface plasmon on the decay dynamics of an excited atom,especially when there is a surface plasmonic-quantum emitter bound state.The main contents of this thesis are as follows:In the first chapter,we mainly introduce some methods for investigating the decay dynamics of an atom around surface plasmonic nanostructures.A brief introduction for the surface plasmon and the optical response model,including the local Drude model,the nonlocal Hydrodynamic Model(HDM)and the generalized nonlocal Optical Response(GNOR)model for metal are given first.Then,we concentrate on the methods for investigating the decay dynamics of an atom in a dissipative nanostructure.Special attention has been paid to the method by the Green's function expression for the evolution operator and the method by solving the non-Markovian Schrodinger equation in the time domain.In addition,the method for calculating the photon Green's function,including the analytical method for nanosphere and numerical method for nanostructure with arbitrary shape,and the method for calculating the energy level shift are introduced to make sure the above two mehtods for decay dynamics work well.In Chapter 2,optical response for metal can be characterized by a complex dielectric function under the local response model,and is usually described by the Drude-Lorentz model based on the classical electron theory.However,it is only in a narrow frequency range that the dielectric function predicted by the above model can agree with the experimental data.In this chapter,we study the energy level shift for a two-level atom in its ground state due to a nearby metallic nanosphere.The difference is shown when the dielectric function for metal is under the Drude mode and from the experimental data.We have found that the dielectric function should be from the experimental data instead of the modeled result in calculating a physical quantity which is related to the optical response in a wide frequency range.In Chapter 3,a bound state between a quantum emitter(QE)and surface plasmon polaritons(SPPs)can be formed,where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time.We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics.We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold.We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system,in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range.With the above two quantities obtained,we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists.A general criterion for identifying the existence of a bound state is presented.The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity.Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value.In addition,it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface,but nearly independent on the size of the nanosphere or the rod.Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.In Chapter 4,by COMSOL multiphysics,the scattered photon Green's functions for a metallic nanosphere,a metallic ellipsoid,and a metallic nanoshell are calculated when the optical response for metal is under the HDM,the GNOR,and the Drude dispersion model.By the methods shown in chapter 3,we study the non-Markovian decay dynamics of an initially excited atom near the above nanostructures,and the existence conditions of bound states when the metal is under the HDM,GNOR and Drude models.The results show that,compared with the results under the Drude model,the spontaneous emission enhancement under the HDM model is greatly suppressed and the peak position is blue-shifted.Comparied with the results under the HDM,the enhancement is further reduced under the GNOR model and the peak position is the same.In addition,it is found that an initially excited atom can reach its stable state much faster under the GNOR model than under the HDM or Drude model.Chapter 5 gives a brief summary and outlook.