Fractional relaxations in photonic crystals (Q2925161)

The authors study the quantum interacting with the radiation field of photonic crystals. The analytical description of the dynamics of the quantum dot interacting with the radiation field of photonic crystals including the population of the exited coherence level and coherence between the two states are examined and discussed. It was shown that the dynamics exhibit a fractional nature via relaxations of the Mittag-Leffler type and that transitions in the long time decays appear. Furthermore, it was shown that the coherence term relaxes according to the decay \(t^{-1/2}\) instead of \(t^{-3/2}\) if the transition frequency of the quantum dot lies exactly in the middle of the band gap. In a similar way, it was shown that the population of the exited level shows a transition from relaxation \(1/t^{3}\) to \(1/t\). Finally, it was shown that these resonances and transitions belong also to the context of matter-wave emissions in optical lattices.