2012/10/25 by Eric Akkermans, Evgeni Gurevich · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Fibonacci number #Fractal #QED vacuum #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Spectrum (functional analysis) #Spontaneous emission #Vacuum state #cond-mat.mes-hall #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1209/0295-5075/103/30009
5 pages, 2 figures
arxiv created 2012/10/25 · openalex publication_date 2013/08/01 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.