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Journal of the Korean Physical Society

Coherent Coupling Between a Three-Level Atom and a Structured Reservoir

Jing-Nuo Wu, Tzong-Jer Yang, Szu-Cheng Cheng

Published Dec 15, 2008• 1 citation
Publisher

Abstract

[[abstract]]We study the spontaneous emission (SE) spectra of a three-level A-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase difference between the air-band and the dielectric-band fields, two band reservoirs become coherent and can interfere with each other. This interference effect depends on the embedded position of the atom and the band-gap width and can affect the SE spectrum. The effect of this interference on the SE spectrum is shown.

DOI
10.3938/jkps.53.3802

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[[abstract]]We study the spontaneous emission (SE) spectra of a three-level A-type atom in photonic crystals. The air-band, the dielectric-band and the free-space vacuum reservoirs coupled with the atom are considered. With the consideration of the phase difference between the air-band and the dielectric-band fields, two band reservoirs become coherent and can interfere with each other. This interference effect depends on the embedded position of the atom and the band-gap width and can affect the SE spectrum. The effect of this interference on the SE spectrum is shown.
The effect of atomic position on the spontaneous emission and optical spectra of a three-level atom embedded in a photonic crystal was studied by considering the coherent two-band photonic-band-gap (PBG) reservoir. With the definite phase difference between the fields of the air band and dielectric band in this coherent PBG reservoir, we found that this coherent property grows stronger and results in the spectrum shift and the appearance of dark lines and kinks as the width of band gap gets smaller; and the variation of the atomic position leads to large shift of spectral peak. The averaged spectra of the system with an ensemble of atoms embedded in the dielectric region are blueshifted while those of atoms in the air region are redshifted. The spectra peaks can even shift more than 75% of the half width at half maximum. The feasible experimental systems composed of an ensemble of molecules (quantum dots or fluorescence dye) in photonic crystals are discussed.
The spontaneous emission of a three-level A-typed atom embedded in anisotropic photonic crystals with two coherent bands is investigated. The relative position of the atom is described by a position-dependent parameter θ( r 0 ), in regard as the coherence of the two bands. The spectrum of the transition in free space vacuum is discussed. The spectral center can be manipulated by the coherent parameter θ( r 0 ), and the spectral intensity can be adjusted via the atomic transition in the coherent photonic reservoir.
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 spontaneous emission spectrum from a driven three-level atom placed inside a double-band photonic crystal has been investigated. We use the model which assumes the upper levels of the atomic transition are coupled via a classical driving field. The transition from one of the upper levels to lower level couples to the modes of the modified reservoir, and the transition from the other upper level to lower level interactwith the free vacuum modes. The effect of classical driving field on the spontaneous emission spectrum of this latter transition is investigated in detail. Most interestingly it is shown that only in the presence of the classical driving field; there is a black dark line in the spontaneous emission spectrum of free-space transition when the modified reservoir is of the photonic band gap type. This dark line is not seen in the case where the modified reservoir is of the free space type for relatively weak driving field.
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.