Abstract
Spontaneous emission of a quantum emitter coupled to a QED vacuum with a
deterministic fractal structure of its spectrum is considered. We show that the
decay probability does not follow a Wigner-Weisskopf exponential decrease but
rather an overall power law behavior with a rich oscillatory structure, both
depending on the local fractal properties of the vacuum spectrum. These results
are obtained by giving first a general perturbative derivation for short times.
Then we propose a simplified model which retains the main features of a fractal
spectrum to establish analytic expressions valid for all time scales. Finally,
we discuss the case of a Fibonacci cavity and its experimental relevance to
observe these results.
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