The Properties Of Spontaneous Emission Of Multi-Level Atom In Non-Markovian Reservoir

The control of atomic spontaneous emission is an active research topic in quantum optics for its potential applications in high precision spectroscopy and quantum information. The atomic spontaneous emission depends not only on the energy level structures of an atom but also on the nature of the surrounding environment to which the atom is coupled. The density of electromagnetic modes in non-Markovian reservoir is distinct to that in vacuum. Thus, the study of decay properties of an atom embedded in these reservoirs can predict some new phenomena to facilitate the understanding of the dynamic behavior of the atom or molecular in non-Markovian system. Consequently, the study is of great meaning from both theoretical and experimental point of view. In this dissertation, we investigate the properties of spontaneous emission of a multi-level atom embedded in microwave cavity and photonic crystals, which are two special kinds of non-Markovian reservoirs.Firstly, we study the interaction between a three-level atom in a configuration and multi-mode cavity fields, and obtain the analytical expression of level-shift operator and atomic spontaneous emission spectrum. In different coupling regime, we investigate the influence of coupling strength between the atom and cavity field on the emission spectrum. It is shown that in strong and intermediate coupling regime, the upper level splits in different ways. In weak coupling regime, the atomic spontaneous emission properties were determined by the cavity decay rate, and the upper level does not split. Furthermore, we find that, as the detuning increasing, the intensity of partial spectrum lines weakens due to the partial inhibition of spontaneous emission.Considering aΛ-type system, in which the two transitions coupled to separate reservoirs, we calculate the upper state population evolution and spontaneous emission spectrum using the resolvent operator under both isotropic and anisotropic dispersion model. It is shown that the atom presents diverse spontaneous emission behaviors under each model. The essence of these phenomena is that each dispersion model corresponds to different coupling strength between the atom and its emitted field.Placing a -type three-level atom in one-dimensional and three-dimensional photonic crystals, respectively, for the case of two transitions were coupled to the same modified reservoir, we obtain the analytical expression of spontaneous emission spectrum, and discuss the influence of relative position of upper band edge to the two lower levels on the emission spectrum. We can get a large population trapping through changing upper band edge position. The corresponding spontaneous emission spectrum shows strong non-Lorentzian line shape.Combining the two ways of controlling atomic spontaneous emission i.e. placing an atom in different circumstances and introducing the external driving field, we study the steady state behavior of a single driven tripod four-level atom. We investigate the influence of detunings on the spontaneous emission spectrum of the atom in free vacuum, and show a few interesting phenomena such as partial spectral-line narrowing and elimination. Placing the atom in photonic band gap reservoir, we study the influence of band gap and detuning of driving field on individual spectrum lines for the different upper band edge positions. When two transition frequencies are far outside the band gap, the photonic band gap does not affect the properties of spectrum lines. The dressed levels tends to be push out the band gap when the two transition frequencies are near the band edge. If the two transition frequencies are deep inside the band gap, the detuning does not affect the atomic spontaneous emission properties.