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Canadian Journal of Physics

Spontaneous emission inhibition from a driven four-level atom in a photonic band gap material

H Zhang, G Q Liu, H Z Zhang

Published Sep 1, 2007• 0 citations
Publisher

Abstract

Two models (an upper levels coupling model and a lower levels coupling model) of a four-level atom embedded in a double-band photonic crystal are adopted. The effect of spontaneous emission cancellation of such systems embedded in different reservoirs are investigated. Especially, the "trapping conditions" of such systems in photonic band gap (PBG) reservoirs are discussed for the first time. We also investigate the different quantum interference effects of the lower levels coupling model embedded in an isotropic PBG reservoir. It is interesting that when the trapping conditions are fulfilled, the additional peaks, which result from the contribution of the additional singularities of Laplace transform of the delayed Green function of the isotropic PBG modes, are eliminated.PACS Nos.: 42.50.Gy, 42.50.Ct, 42.70.Qs

DOI
10.1139/p07-093

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Two models (an upper levels coupling model and a lower levels coupling model) of a four-level atom embedded in a double-band photonic crystal are adopted. The effect of spontaneous emission cancellation of such systems embedded in different reservoirs are investigated. Especially, the "trapping conditions" of such systems in photonic band gap (PBG) reservoirs are discussed for the first time. We also investigate the different quantum interference effects of the lower levels coupling model embedded in an isotropic PBG reservoir. It is interesting that when the trapping conditions are fulfilled, the additional peaks, which result from the contribution of the additional singularities of Laplace transform of the delayed Green function of the isotropic PBG modes, are eliminated.PACS Nos.: 42.50.Gy, 42.50.Ct, 42.70.Qs
The two models of three-level (one upper level and two lower levels, or two upper levels and one lower level) atom embedded in a double-band photonic crystal are adopted. The atomic transitions from the upper levels to the lower levels are assumed to be coupled by the same reservoir which are respectively the isotropic photonic band gap (PBG) modes, the anisotropic PBG modes and the free vacuum modes. The effects of the fine structure of the atomic ground state levels in the model with one upper level and two lower levels and the quantum interferences in the model with two upper levels and one lower level on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interferences induce additional narrow spontaneous lines near the transition from the empty upper level to the lower level.
The impacts of an external driving field on the spontaneous emission from an excited two-level atom embedded in a double-band photonic crystal is investigated. In the upper level coupling, a dark line occurs, which stems from deductive quantum interference induced by the external driving field. The dark line appears with an additional peak when it is outside the band gap of the PBG reservoirs. The dark line cannot be seen when it falls into the band gap. In the case of lower level coupling, interference plays no role. The emission spectrum displays two incoherent modified Lorentzian lines that have two singularities in each side of the band gap in isotropic PBG reservoirs.
A model of a four-level atom embedded in a double-band photonic crystal (PC) is presented. The atomic transitions from the upper two levels to the lower two levels are coupled by the same reservoir which is assumed in turn to be isotropic PC modes, anisotropic PC modes and free vacuum modes. The effects of the fine structure of the atomic ground state levels and the quantum interference on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown for the first time that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PC case. Quantum interference induces additional narrow spontaneous lines near the transition from the empty upper level to the lower levels.
The spontaneous emission spectrum from a four-level atom in a double-band photonic crystal has been investigated. We use the model which assumes three atomic transitions. One of the transitions interacts with the free vacuum modes and the other two transitions couple to the modes of the isotropic photonic band gap (PBG), the anisotropic PBG and another free vacuum. The effects of the fine structure of the lower levels on the spontaneous emission spectrum of an atom are investigated in detail in the three cases. New features of four (two) transparencies with two (one) spontaneous emission peaks, resulting from the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.
The spontaneous emission spectrum from a V-type three-level atom embedded in a double-band photonic band gap (PBG) material has been investigated for the first time. Most interestingly it is shown that there is not only a black dark line, but also a narrow spontaneous line near the edges of the double photonic band. The positions of the dark line and narrow spontaneous line are near the transition from an empty upper level to a lower level. The lines stem from destructive and constructive quantum interferences, which induce population transfer between the two upper levels, in the PBG reservoirs. The effects of system parameters on the interference have been discussed in detail.
Quantum interferences in spontaneous emission spectrum from a V-type three-level and a double V-type four-level atom embedded in a double-band photonic band-gap material have been investigated. We demonstrate that there is not only a black dark line, but also a narrow spontaneous line in the spectrum. The dark line results from a destructive interference or singularities of the density of states of the radiation field. The narrow spectral line arises from a population transfer under joint constructive interferences. The spontaneous emission spectrum is compared to the cases of single-band and double-band photonic band-gap reservoirs.