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Journal of Modern Optics

Spontaneous emission from a three-level atom embedded in anisotropic photonic band gap structures

Hiroyuki Nihei, Atsushi Okamoto

Published May 8, 2004• 7 citations
Publisher

Abstract

We investigate spontaneous emissions from a three-level atom embedded in realistic anisotropic photonic band gap structures, where the band edge is assumed to be midway between the two upper levels of the atom. In the anisotropic model, the atom-field interaction is reduced to be smaller than that in the ideal isotropic model, which results in the reduction of suppression and oscillation effects in the spontaneous emission; however, we demonstrate that the suppression is strongly enhanced even in the anisotropic model by expanding the detuning between the upper level and the band edge, while the oscillation is greatly reduced. This demonstration is carried out by calculating the atomic state vector for a wide range of the detuning. Using the state vector, the atom-field interaction is studied for two field parts, a localized part and a propagating part, separately. For the localized part, the atom-field interaction is enhanced by expanding the detuning, in spite of the anisotropy, which leads to a strong suppression effect, while for the propagating part, the atom-field interaction is reduced, which leads to a weak oscillation effect. This result is relevant to strong memory effects with high-speed switching, which are attractive properties for a qubit.

DOI
10.1080/09500340408232506

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We investigate spontaneous emissions from a three-level atom embedded in realistic anisotropic photonic band gap structures, where the band edge is assumed to be midway between the two upper levels of the atom. In the anisotropic model, the atom-field interaction is reduced to be smaller than that in the ideal isotropic model, which results in the reduction of suppression and oscillation effects in the spontaneous emission; however, we demonstrate that the suppression is strongly enhanced even in the anisotropic model by expanding the detuning between the upper level and the band edge, while the oscillation is greatly reduced. This demonstration is carried out by calculating the atomic state vector for a wide range of the detuning. Using the state vector, the atom-field interaction is studied for two field parts, a localized part and a propagating part, separately. For the localized part, the atom-field interaction is enhanced by expanding the detuning, in spite of the anisotropy, which leads to a strong suppression effect, while for the propagating part, the atom-field interaction is reduced, which leads to a weak oscillation effect. This result is relevant to strong memory effects with high-speed switching, which are attractive properties for a qubit.
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.
We have studied the properties of the spontaneous emission from a two-level atom embedded in two-band photonic crystals. Due to the anisotropic two-band dispersion relation, the localized and propagating fields cannot coexist, this leads to the non-quasi-oscillation behaviour of the upper level population. Thus the upper level population will tend to a constant as time goes to infinity, or decay with time in a power law, or decay with time exponentially, different from that in the isotropic one-band dispersion relation case. These properties are directly related to the relative position of the upper level from the band edge and the width of the gap.
The spontaneous emission from a three-level atom embedded in a photonic band gap structure is studied. Interference between two transitions leads to quasiperiodic oscillations of population between the two upper levels with large amplitudes. The spontaneous emission of the atom is characterized by three components in the radiated field: a localized part, a traveling pulse, and a (1/t)3(1/\sqrt{t}{)}^{3}(1/t​)3 decaying part. An analytical expression for the localization distance of the localized field is obtained. The energy velocity for the traveling pulse could be close to zero. By selecting an appropriate initial superposition state, a large amount of population trapping can be achieved.
The spontaneous emission from a microwave-driven four-level atom embedded in an anisotropic photonic crystal is studied. Due to the modified density of state (DOS) in the anisotropic photonic band gap (PBG) and the coherent control induced by the coupling fields, spontaneous emission can be significantly enhanced when the position of the spontaneous emission peak gets close to the band gap edge. As a result of the closed-loop interaction between the fields and the atom, the spontaneous emission depends on the dynamically induced Autler–Townes splitting and its position relative to the PBG. Interesting phenomena, such as spectral-line suppression, enhancement and narrowing, and fluorescence quenching, appear in the spontaneous emission spectra, which are modulated by amplitudes and phases of the coherently driven fields and the effect of PBG. This theoretical study can provide us with more efficient methods to manipulate the atomic spontaneous emission.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.