Spontaneous Emission Of A Two-level Atom Interacting With The Field Of A Semi-infinite Rectangular Waveguide

We study a quantum electrodynamics system made of a fixed two-level atom and a semi-infinite rectangular waveguide,which behaves as an ideal boundary in one end.The problem of spontaneous emission of a two-level atom is discussed.Unlike free space,the dispersion relation of a semi-infinite rectangular waveguide is nonlinear,there is a cut-off frequency,and there are many transverse modes in the waveguide,and each transverse mode has a cut-off frequency.There are two kinds of waves propagating in the semi-infinite rectangular waveguide,namely the transverse wave(TE)and the transverse magnetic wave(TM),in this paper,we assume that the dipole moment of the two-level atom is in the direction of the z,so the atom is only coupled to the TM mode.Based on these features,the atomic transition frequency ?0 increase gradually from low to high.When ?0 is lower than the minimum transverse mode's cutoff frequency ?1,according to the Wiger-Weisskopf approximation,we found that the spontaneous emission of the atom is suppressed;When ?0 is very close to ?1,the atom rapidly decays from the excited state to the ground state;When ?0 add to the between the first and second transverse mode cut-off frequency ?1,?2,but not close to the two cut-off frequency value,the atom interacts with one transverse mode;When ?0 continue to increase to more than ?2,and very close to ?2,at this point,there are two modes interact with atoms.According to the Wiger-Weisskopf approximation,it is found that the second wave modes will quickly decay the atom from the excited state to the ground state.We consider the case of an atom interacting with only one transverse mode,namely TM11 mode.When the transition frequency of the atom is far away from the cutoff frequency ?1 by linearly expanding the dispersion of the light field,we found that when the distance between the boundary of the waveguide and the atom is not 0,that is,the atom is not at the boundary of the waveguide,the number of atoms in the excited state will appear to deviate from exponential decay,show us the oscillation,there will be one or more peaks,and the size of the peak decreases with time;When the atom is at the boundary of the waveguide,it back to the exponential decay with time.Compared with the linear waveguide,we use the dispersion of the light field in the vicinity of the cutoff frequency to the wave vector of the quadratic method to study the spontaneous emission of atom.We find that as long as the distance from the atom to the boundary is 0,the probability amplitude of an atom in an excited state will decay exponentially,but at the energy of q2 the attenuation is slow,and always find a real energy,which means that in the secondary waveguide,there will be a bound state in which the atom is in an excited state,however,there is no linear waveguide.The full text is divided into four parts:The first chapter is an introduction.This chapter mainly introduces the defi-nition of atomic spontaneous emission,the positive role of spontaneous radiation in completing quantum information task,and the current research and significance.In addition,the Green function is analyzed.The second chapter firstly introduce the basic connotation of Heisenberg quan-tized thought,then we obtain two kinds of transverse waves in a half infinite rect-angular waveguide,TE wave and TM,at last,guided by the Heisenberg quantized idea,the quantization of the semi-infinite rectangular waveguide is derived.In the third chapter,we study the variation of the number of excited states of a stationary two-level atom in a semi infinite rectangular waveguide with time.and then,in the single particle excitation space,the relationship between the wave func-tion at any time of the system and the wave function of the initial moment is written by the green function,the equation for the probability that the atom is in an excited state is obtained.The spontaneous emission of the atom is studied by calculating the number of atomic excited state.Then we study the characteristics of the spontaneous emission of the atom by two methods,namely the Weisskopf-Wigner approximation method and the method of expanding the dispersion relation of the light field to the two power of the wave vector.The fourth chapter makes a summary of the whole article,and puts forward some prospects for the future work.