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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Super-radiance and decay localized excitations in the linear equidistant system of N two-level atoms

E. A. Gavrilenko, А. И. Зайцев

Published Mar 3, 2008• 0 citations
Publisher

Abstract

We investigate the super-radiance decay of localized excitation in the line of two-level atoms. It is demonstrated that the excitation is underradiated. The residual part forms polarization waves propagating from areas of residual excitation to the line edge.
DOI
10.1117/12.801745

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The polarization properties and the temporal shapes of the super-radiance pulses formed on degenerate levels are studied theoretically in a semiclassical approximation. The dependence of the super-radiance pulse polarization on the values of the total angular momenta of resonant levels and on the polarization and area of the pumping pulse is examined in detail. Non-linear equations describing the temporal shapes of the super-radiance pulses with different polarizations are obtained. Some examples with low values of angular momenta of the levels are discussed. It is shown that, in general, the temporal shape of the super-radiance pulse differs from hyperbolic secant.
The existence of sub-radiance is demonstrated for a generalized rotating-wave approximation Dicke Hamiltonian model characterized by an arbitrary space dependence of the coupling constants of N two-level atoms to a single mode of a radiation field. To deduce this result we first establish the form of a characteristic equation for sub-radiance and then solve it by introducing a suitable non-unitary operator. In this way the explicit form of all the sub-radiant states of the spatially extended model are easily obtained from those that are well known and relative to the point-like Dicke model. Our investigation clearly shows that inhomogeneous coupling of the N atoms with the field is compatible with sub-radiant behaviour.
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Using eigenmode analysis I calculate in the linear regime the emission characteristics from a slab of two-level resonant atoms excited by a delta-pulse propagating normal to the surface of the slab. I show that the qualitative features of the emitted spectra in the forward and backward directions to be different from each other; I also find the effects of the total linewidth of the resonance line and of the deviation in the spatial periodicity of the initial atomic polarization from k 0, where k 0 = ω0/c and ω0 is the two level resonant frequency, on the spectra. The dominant spatial mode of the system is identified as the key parameter for determining the forward emission spectral width.