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arXiv:quant-ph/0009106 · Physical Review A

Coherent phenomena in photonic crystals

Dimitris G. Angelakis, Emmanuel Paspalakis, P. L. Knight

Published May 29, 2001• 85 citations
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Abstract

We study the spontaneous emission, absorption, and dispersion properties of a \ensuremath{\Lambda}-type atom where one transition interacts near resonantly with a double-band photonic crystal. Assuming an isotropic dispersion relation near the band edges, we show that two distinct coherent phenomena can occur. First the spontaneous emission spectrum of the adjacent free-space transition obtains ``dark lines'' (zeros in the spectrum). Second, the atom can become transparent to a probe laser field coupling to the adjacent free-space transition.

DOI
10.1103/physreva.64.013801

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We study the spontaneous emission, absorption, and dispersion properties of a \ensuremath{\Lambda}-type atom where one transition interacts near resonantly with a double-band photonic crystal. Assuming an isotropic dispersion relation near the band edges, we show that two distinct coherent phenomena can occur. First the spontaneous emission spectrum of the adjacent free-space transition obtains ``dark lines'' (zeros in the spectrum). Second, the atom can become transparent to a probe laser field coupling to the adjacent free-space transition.
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.
Summary form only given. The majority of studies of quantum optical processes occurring in atoms interacting with modified reservoirs, such as microcavities and photonic band gap materials, have concentrated on spontaneous emission dynamics. In this paper we report our recent theoretical results on absorption and dispersion dynamics of a A-type system where one transition spontaneously decays in a two band photonic reservoir. The coupling to this modified reservoir leads to a non-Markovian spontaneous decay of the atomic state, which in return influences the dispersion and absorption properties of a probe laser pulse coupling to the other atomic transition.
The probe absorption–dispersion spectra of a driven three-level atom in a double-band photonic crystal have been investigated. We use the model which assumes the upper levels of the atomic transitions coupled via a classical driving field. One of the transitions interacts with the free vacuum modes, and the other transition couples to the modes of the modified reservoir (photonic band gap). The effect of the classical driving field on the absorption–dispersion spectra 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, and slow group velocities are obtained near the transparency window.
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 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.