Spontaneous Emission Of A Three-level Atom Embedded In 1D LHM And RHM Photonic Crystals

Atomic spontaneous decay is a fundamental object in quantum optics. It refers to that an atom can jump from its excited state down to its ground state spontaneously due to the vacuum fluctuation, and emits a photon. Such photon has no steady phase and direction. So the spontaneous of atom has no merit to the generation of laser and the coherence of atom and light, needed to be controlled and inhibited. It is well known that spontaneous emission depends not only on the energy structure of the atom but also on the nature of the surrounding environment, more specifically, on the density of states (DOS) of the radiation. To control atomic spontaneous decay, John and Yablonovitch suggested Photonic Crystal, in which the photonic band gap and localization of photons can strongly change the DOS of the vacuum field. It has attracted the word. Almost at the same time, a new fabricated material called Left-Handed Metamaterials (LHM) attracts a great deal of attention, which have negative permittivityμand negative permeabilityεsimultaneously. With the help of that, there are great deal of unusual phenomena, such as negative refractive index, reverse Snell's Law, a reverse Doppler shift, reverse Cerenkov radiation and perfect lens and so on, when the light transfer. LHM and RHM photonic crystals which are combinations of the two new materials, are studied in this paper. We take the condition of one dimension and research Spontaneous emission of a three-level atom embedded in one-dimensional LHM and RHM photonic crystals in detail.There are three major parts in this paper:1. Give the basis of choosing the one-dimensional LHM and RHM photonic crystals in theory. With the transfer matrix, we investigated electromagnetic transmission, approve that there are zero average refractive index photon band gaps except for classical photonic band gaps. The differences of them are analyzed: greater width of photonic gaps, not sensitive to the angle of incidence and periodical thickness. So they can restrain atomic spontaneous emission effectively. These provide perfect conditions to control atomic spontaneous emission.2.ω_k = A +B cos( kT), a new form of the dispersion relation--- is used in the calculation of atomic spontaneous radiation fluorescence spectra, which is effective in LHM and RHM photonic crystals and normal photonic crystals. With the help of the new dispersion relation, calculation of atomic spontaneous radiation fluorescence spectra in the tow type photonic crystals can boil down to a unified form. Thus the differences of LHM and RHM photonic crystals and normal photonic crystals in the calculation of atomic spontaneous emission are the different expressions of . At last we find the relationship between the crystal structure and A--- the center frequency of photonic band in the first Brillouin zone of one-dimensional photonic crystals. The relationship between A and the angle of electromagnetic radiation, periodical thickness, the thickness of each component in the tow type photonic crystals are different. And the larger left-handed materials component impedance, the more obvious differences between the two photonic crystals. In the perspective of the smaller angle of radiation, A's dependence is little. Whenθis large enough, A rises rapidly with the augmentation of the angle. Further more, when the one-dimensional LHM and RHM photonic crystals are zero average refractive index photonic crystals,A is the maximum. Two different values of A can be used to control the spontaneous radiation of different atoms.3. We carry out a detailed study on the spontaneous radiation of V-type three-level atom embedded in the edge of bands of one-dimensional LHM and RHM photonic crystals. Using interact Hamiltonian and Schrodinger Equation, by means of Laplace transform, with the dispersion relation and the photon density of states, we obtain the spontaneous spectrum equation from the probability amplitude equation varies to time and discussed the effect of parameters of the system to the spontaneous fluorescence spectra. It is show that spontaneous emission depends not only on the properties of the external field but also on the nature of the surrounding environment (such as vacuum field or Photonic Crystal). The spontaneous emission fluorescence spectra of V-type three-level atom embedded in one-dimensional LHM and RHM photonic crystals is different from that in the vacuum field. There is no radiation when the transition frequency at the edge of the band because of the photonic band gaps .And the especial density of states at the edge of the band result in very narrow small spontaneous emission peaks. In the case of that an atom is equally and synchronously pumped to the two upper levels and symmetric values of parameters for the two transitions are employed, when the coupling coefficient between the two transitions is 1, namely the quantum interference is maximal between the two transitions, while quantum interference and odd points of the density of states (DOS) bring on dark lines at the point ofδk= 0. When initial atom only at the highest level, a dark line appear at the other transition frequency, but two small spontaneous emission peaks will be in the vicinity of the dark line. One narrower than in vacuum and the other is smoother. With the augmentation of the coupling coefficientη23, the intension of the two spontaneous emission peaks increases, the width keeps the same, and the total radiation intensity increases, whereas the width decreases and the total radiation intensity keeps the same in vacuum. That is because of the PBG of one-dimensional LHM and RHM photonic crystals. The coupling constants are the reasons of the acutance of the spontaneous emission peak. The smaller the coupling constant is, the more acute the corresponding peak is. When atomic transition frequency close to the edge of photonic band gaps, spontaneous emission peaks get narrower and smaller, that is obviously.Compared to previous work, we introduce a new form of dispersion relations in photonic crystal, which is effective in LHM and RHM photonic crystals and normal photonic crystals in this paper. With that, we find a method to calculate the atomic spontaneous radiation in one-dimensional LHM and RHM photonic crystals and discuss on the effects of the system parameters on the spontaneous emission in detail. The calculation of a three-level atomic spontaneous emission in LHM and RHM photonic crystals has been considered for the first time. It establishes the physical basis for the application of new materials such as Left-Handed Metamaterials and Photonic Crystals, consummates "theory of light and matter interact" in non-free vacuum field, and deepen people's acquaintanceship to properties of quantum optical in different circumstances。...