Spontaneous Emission From A Three-Level Atom With Lower Level Coupling In An Anisotropic PBG

Photonic crystal (photonic band gap material) is an artificial synthetic material which is made up of materials of different refractive indexes by micro-period structure. The best characteristic of this material is the photonic band gap, which means frequencies in the forbidden gap are strictly forbidden transmitting. Since E. Yablonovitch and S. John proposed the photonic crystal conception respectively in 1987, photonic crystal has become the hot spot of scientific research due to its distinctive physical features. And the spontaneous emission from atom embedded in it has always been the hot researching topic in quantum optics because of the interesting physical phenomena it can cause, such as electromagnetically induced transparency.Spontaneous emission is a kind of process that atom in excited state can transit to the ground state spontaneously without incoming photons in free vacuum space. From Becquerel first observed spontaneous emission phenomenon in 1896, to Einstein proposed spontaneous emission related theory, and long after that, people thought spontaneous emission was a physical process which was inherent in the atomic system, spontaneous, irreversible, and we could not control it. But as quantum radiation theory develops, people recognize that spontaneous emission depends on not only the atomic structure, but also the environment which the atom is embedded in.So at first, the investigation on spontaneous emission has been concentrated on the free vacuum reservoir and the research on the photonic crystal is not enough. Nowadays, research on spontaneous emission from an atom embedded in photonic crystal focuses on the cases without driven fields. So this paper does some theoretical research on spontaneous emission from a three-level atom embedded in an anisotropic PBG with lower level coupling. Including:1. In my theoretical derivation, I use quantum theory of atom-field interaction and turn mode density of field in photonic crystal into G function which is closely related to photonic crystal structure. I obtain the population expression using dressed state, Laplace transform and residue theory and then derive the emitted field and spontaneous emission spectrum.2. I discuss the property of spontaneous emission from an atom with lower level coupling in detail for the first time. It includes population evolution, radiated field distribution, and spontaneous emission spectrum line type.3. I investigate the effect on spontaneous emission for different parameters, such as the detuning between the carrier frequency of the driven field and the atomic resonant frequency.I have investigated the properties spontaneous emission from a three-level atom with lower-level coupling in an anisotropic photonic crystal. We find that the time-evolution properties and the components of the radiation fields depend on not only the relative position between the upper level of the atom and the band edge, but also the intensity of the driven field, the detuning between the atomic resonant frequency and the carrier frequency of the driven field.Emitted field could be divided into three kinds: diffusion field, localized field, and propagating field. In region I, there are localized fields which do not decay with time. In region II, there are localized field which decays with time and propagating field. In region III, there are propagating fields which decay with time. Because of the existence of the photonic crystal, there is quantum interference between propagating field and diffusion field, which leads to the oscillation of the intensity of the total field. And with the increase of the distance from the atom, the interference gets weaker.Because of the different distribution of emitted field, in region I, there is almost no decay of population; in region II, the population slowly decays with time; in region III, the population decays fastest.I also find that spontaneous emission spectra are different among regions. In region I, spectra consist of two localized mode singularities and one peak at the band edge. In region II, there is one peak when r is comparatively large. In region III and IV, there are two peaks which do not change as r grows.