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Journal of Modern Optics

Collective behaviour in a system of two two-level atoms at the edge of a photonic band-gap

Georgios M. Nikolopoulos, P. Lambropoulos

Published Jan 1, 2002• 9 citations
Publisher

Abstract

We study the behaviour of two closely spaced two-level atoms near-resonantly coupled to the edge of a photonic band-gap continuum.The problem is solved by means of the discretization technique, while a four-level configuration is adopted for the interpretation of the numerical results. The role of the dipole-dipole interaction in the enhancement of the collective decay is investigated. We show that under special circumstances the generation of an entangled antisymmetric state of the two two-level atoms is possible.

DOI
10.1080/09500340110065772

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We study the behaviour of two closely spaced two-level atoms near-resonantly coupled to the edge of a photonic band-gap continuum.The problem is solved by means of the discretization technique, while a four-level configuration is adopted for the interpretation of the numerical results. The role of the dipole-dipole interaction in the enhancement of the collective decay is investigated. We show that under special circumstances the generation of an entangled antisymmetric state of the two two-level atoms is possible.
We extend recent work on two closely spaced atoms interacting through the narrow band of strongly coupled modes at the edge of a photonic band gap. The resonant dipole-dipole interaction (RDDI) is strongly modified for atomic transition frequencies in the vicinity of the band-gap edge, but we show that an analytical approximation to the RDDI agrees very well with the exact RDDI obtained by numerical integration using the exact dispersion relation. Having established the value of the RDDI, we can derive the amplitudes for the two atoms without resorting to the pole approximation which is necessary due to the strongly modified mode structure in the dielectric host. For a wide range of parameters we find beating and population trapping in the long time limit. The distribution of population in the photonic continuum is investigated in the long time limit in the case of one and two atoms. It is found to be strongly asymmetric and to exhibit a strong signature of the unusual mode structure in the material at the band-gap edge.
We study spontaneous emission in an atomic ladder system, with both transitions coupled near resonantly to the edge of a photonic band gap continuum. The problem is solved through a recently developed technique and leads to the formation of a two-photon +++ atom bound state with fractional population trapping in both upper states. In the long-time limit, the atom can be found excited in a superposition of the upper states and a direct two-photon process coexists with the stepwise one. The sensitivity of the effect to the particular form of the density of states is also explored.
The coherent control of cooperative spontaneous emission from two identical non-overlapping three-level atoms in the V-configuration located within a photonic band gap (PBG) material with two resonant frequencies near the upper band edge of the PBG and confined to a region small in comparison to their radiation wavelengths but still greater than their atomic sizes is investigated. The dependencies of cooperative effects in which a photon emitted by one atom is reabsorbed by the other atom on the inter-atomic separation, on the initial state of the two-atom system, on the strength of the driving control laser field, and on the detuning of the atomic resonant frequencies from the upper band edge frequency is analyzed so as to identify the conditions for which these cooperative effects are enhanced or inhibited. Cooperative effects between atoms are shown to be influenced more by the PBG than by the nature of the atomic transitions involved. Excited state populations as well as coherences between excited levels are expressed in terms of time-dependent amplitudes which are shown to satisfy coupled integro-differential equations for which analytic solutions are derived under special conditions. Unlike for the case of one atom in a PBG where the fractional non-zero steady state populations on the excited levels as well as the coherence between the excited levels are constants independent of time, in the case of two atoms in PBG these quantities continuously oscillate as a manifestation of beating due to the continuous exchange between the two atoms of the photon trapped by the PBG. The values of these quantities as well as the amplitudes and frequencies of their oscillations depend of the parameters of the system, providing different ways of manipulating the system. The general formalism presented here is shown to recapture the special results of investigations of similar systems in free space when the non-Markovian memory kernels of the PBG are replaced by delta function dependent Markovian memory kernels.
We studied the effects of a coherent monochromatic resonant laser field driving the transition of a two-level atom embedded in a photonic band gap (PBG) material on the emission dynamics of the atom. When the transition frequency of the atom lies outside a PBG and sufficiently far from the band edge that the emission dynamics of the atom is not normally affected by the gap, the dynamic stark splitting of the upper level of the atom into two dressed states by a sufficiently strong resonant driving field can bring the lower dressed state close enough to the band edge or even inside the gap so as to be affected by the gap, providing a switchable means of extending the novel effects of atom–photon interaction near the edge of a PBG for atomic transitions outside the gap and far from the band edge. The net effect is as if a sufficiently strong resonant field driving a transition of an atom embedded in a PBG actively shifts the PBG close enough to the transition so that the gap affects the emission dynamics associated with the transition.
We describe the collective optical properties of impurity two-level atoms in a photonic band gap interacting by resonance dipole-dipole interaction (RDDI) and coupled to a localized cavity mode. The random impurity atom positions are modeled by means of a Gaussian random distribution of RDDI's with variance JJJ and atomic line fluctuation with variance $\ensuremath{\delta}$. We demonstrate the occurrence of a new collective atomic steady state, the optical analog of a spin-1/2 dipolar glass, and an associated Bose-glass state of photons in the cavity mode.