Superradiance of Frenkel excitons in linear systems

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Abstract
Dicke’s superradiance from a gas system of atoms and molecules was described in terms of two-level atoms, i.e., as an assembly of half-spin operators. In this system the magnitude of the total spin, which is called a cooperation number, is conserved at the maximum for the whole radiative process. We will answer in this paper how this superradiance is modified in the crystal in which an excitation can propagate from atom to atom through dipolar interactions. As a prototype of a crystal, we choose a linear chain of two-level atoms. The superradiance master equation of this system can be solved in terms of the exact solution of Lieb, Shultz, and Mattis for the spin system. The first effect is that the emitted frequency shows opposite shifts red and blue, respectively, for the first and second halves of the superradiance pulse, or vice versa, depending upon the sign of the transfer-matrix element of the excitation. The second effect is the appearance of a slow component in the emission tail, which originates from mixture of the states with smaller cooperation numbers or smaller oscillator strength under the transfer of the excitations. These results are demonstrated for a mesoscopic system of linear chains.