Superradiance of Excitons in Mesoscopic Systems
Dicke’s  superradiance from a gas system of atoms and molecules was described in terms of a two-level system, i.e., as an assembly of half-spin operators. Then 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 a crystal in which an excitation can propagate from atoms to atoms through dipolar interactions. As a crystal prototype, 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 chirping, i.e., the emitted frequency shows opposite shifts of 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 the slow component of 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 linear chain mesoscopic system.
KeywordsSlow Component High Harmonic Generation Mesoscopic System Frenkel Exciton Transfer Matrix Element
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