Study On The Non-Markovian Process And The Angular Distribution Of The Spontaneous Emission Of A Two-level Atom Embedded In Multi-layered Media

The atomic spontaneous emission (SpE) phenomenon is a fundamental problem in quantum optics. Since the spontaneous emission is the origins of the quantum noise, the research to control the SpE becomes importance in laser physics and technology. There are some main approaches to change the SpE, for example, (1) changing the coupling spectrum between the atom and reservoir; (2) using the quantum interference effect between the different transition channels; (3) by the quantum measurement. In this paper, we study the non-Markovian spontaneous emission process of a two-level atom embedded in stratified medium.In chapter 2, we investigate the non-Markovian memory function of a two-level atom embedded in multi-layered media. According to the Weisskopf-Wiger theory, the spontaneous emission decay in the free space is following an exponential decay law with the constant decay rate. This conclusion is suitable for the stable decay after sufficient long time. In the initial stage of the SpE, the process is in fact a non-Markovian process, so the W-W approximation is not true. We find that in the early stage, the spontaneous decay process is dependent on the history of SpE and the instantaneous decay rate is a function of the time. In the first several optical cycles of the atomic transition, the memory effect in the SpE can not be neglected. This memory effect can be described by a non-Markovian memory function. We use a complete set of mode functions for the multi-layered media to quantize the field, and solve the dynamic equation of the SpE decay. The non-Markovian memory function is defined to deal with the spontaneous emission of a two-level atom embedded in the multi-layered media. It is shown that the memory function is related to the Fourier transform of the reservoir coupling spectrum. In the early stage of the SpE, the memory function falls down quickly from a sharp peak. The width of this peak describes the memory time in the non-Markovian SpE process. When the SpE field goes back to the atom, the atom feels the presence of the environment, there are some pulse-like sudden changes arising in the memory function, and the amplitudes become weak with time, so the memory effect becomes more and more faint. We find that the memory time depends on the width of the reservoir coupling spectrum. The wider the spectrum is, the shorter the memory time.In chapter 3, the angular distributions of SpE decay rate of a two-level atom placed in the multi-layered structure is investigated. In the stable decay stage, based on the Weisskopf-Wiger approximation, we get some numerical results on the angular distributions for the decay rate in the micro-cavity of three classes 1DPCs. It is shown that the angular distributions of SpE decay rate is determined by the structure of 1DPC, the orientation of the atomic dipole moment and the position of the atom in the cavity. If the dipole moment is parallel to the interface of the slabs, both TE and TM components of the emission field contribute to decay rate, andangular distributions is a function of the angleθandφ. If the dipole moment isalong to the normal of the interfaces, the decay rate is contributed only by TM component of the field, and angular distributions depend on the angle 6 and have symmetry around the axis normal to the interfaces of the 1DPC structure.