Spontaneous Emission from a Fractal Vacuum

TL;DR

This paper investigates how a quantum emitter's spontaneous emission behaves when coupled to a fractal-structured vacuum, revealing non-exponential decay with power-law and oscillatory features influenced by the fractal spectrum.

Contribution

It introduces a theoretical framework for understanding spontaneous emission in fractal spectra and provides analytic models capturing the full time evolution of decay.

Findings

Decay follows a power law rather than exponential

Oscillatory behavior depends on local fractal properties

Analytic expressions valid for all time scales are derived

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.