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Journal of Physics B Atomic Molecular and Optical Physics

Effect of a modified reservoir on the nature of interference in the spontaneous emission of a driven four-level atom

Samad Roshan Entezar, Hamid Vahed, H. Tajalli

Published Jul 6, 2007• 7 citations
Publisher

Abstract

The effect of a modified reservoir on the nature of the quantum interference in the spontaneous emission of a driven double V-type four-level atom has been investigated. In the model used, the double V-type transitions of a driven atom interact respectively with a free vacuum reservoir and a modified reservoir, leading to the two possible types of quantum interference. The results show that the construction or the destruction of interference in the free vacuum reservoir depends on the type of the modified reservoir and the absence or the presence of interference in the modified reservoir. More interesting, it is shown that based on the presence or the absence of interference in the modified reservoir, interference in the free vacuum reservoir can be constructive or destructive if the modified reservoir is of the type of the free vacuum reservoir. On the other hand, the interference in the free vacuum reservoir is constructive, regardless of the presence or the absence of interference in the modified reservoir, if the modified reservoir is of the type of the photonic band gap. This case, therefore, can be used to control effectively the spontaneous emission and absorption spectra.

DOI
10.1088/0953-4075/40/14/011

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The effect of a modified reservoir on the nature of the quantum interference in the spontaneous emission of a driven double V-type four-level atom has been investigated. In the model used, the double V-type transitions of a driven atom interact respectively with a free vacuum reservoir and a modified reservoir, leading to the two possible types of quantum interference. The results show that the construction or the destruction of interference in the free vacuum reservoir depends on the type of the modified reservoir and the absence or the presence of interference in the modified reservoir. More interesting, it is shown that based on the presence or the absence of interference in the modified reservoir, interference in the free vacuum reservoir can be constructive or destructive if the modified reservoir is of the type of the free vacuum reservoir. On the other hand, the interference in the free vacuum reservoir is constructive, regardless of the presence or the absence of interference in the modified reservoir, if the modified reservoir is of the type of the photonic band gap. This case, therefore, can be used to control effectively the spontaneous emission and absorption spectra.
In this paper, the probe absorption spectrum of a four-level atom in photonic crystals has been investigated. A model is used, which assumes the transitions from the two upper levels to one of the lower levels coupled to the modes of the modified reservoir (photonic band gap) and transitions from the two upper levels to the other lower level coupled to the free vacuum modes. The effect of quantum interference in spontaneous emissions from the two upper levels to the lower levels on the absorption spectrum of an atom is investigated in detail. Most interestingly, it is shown that the atom becomes transparent to a probe laser field coupled to the free space transition only in situations where complete quantum interference takes place in both the free space transitions and the modified reservoir transitions.
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.
The probe absorption-dispersion spectrum of a double V-type four-level atom in a double-band photonic crystal is investigated. In the model used, the double V-type transitions are, respectively, coupled by the free vacuum modes and the photonic band gap modes, leading to the two possible types of quantum interference. Three types of zero absorption (transparency) appear in this model. In the first type, there exist two zeroes at the band edge frequencies in the case of isotropic photonic band gap. In the second type, a zero emerges at the middle frequency of two upper levels in the case that the quantum interference takes place in both V-type transitions. Finally, in the third type, a zero occurs at or around the middle frequency of two upper levels in the case that the quantum interference takes place only in the V-type transitions coupled to the free vacuum modes. Ultimately, the probe absorption-dispersion spectrum in the case of the single-band photonic band gap reservoirs compared to those of the double-band photonic band gap reservoirs. The results show that the dispersion property of the system depends on the two types of the quantum interference and the density of states of the photonic band gap reservoir.
Quantum interferences in spontaneous emission from a double V-type four-level atom in a double-band photonic crystal have been investigated. The double V-type transitions from the two upper levels to the two lower levels can interact not only with modes near the edges of a double-band photonic band gap, but also with free vacuum modes. The resulting two types of quantum interferences give rise to not only dark lines, but also a narrow spontaneous line in the spectrum from the transition coupled to the free vacuum modes. The dark lines and narrow spontaneous line are shown to be dependent on the width of the forbidden gap, relative position of the upper levels from the band edges, coupling constants, and initial coherent superposition state of the system.
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.