Fractional decay in the spontaneous emission of a two-level system

TL;DR

This paper investigates how the survival probability of a two-level quantum system's spontaneous emission scales with time in environments with specific spectral properties, revealing fractional decay behaviors and implications for the quantum Zeno effect.

Contribution

It introduces a novel analysis of fractional decay scaling in two-level systems interacting with environments having bounded spectra, highlighting the dependence on spatial dimension and energy dispersion.

Findings

Survival probability scales as 1 - α t^{2 - D/n} at short times.

Long-time decay follows α t^{D/n - 2}.

Implications for the quantum Zeno effect with modified Zeno times.

Abstract

We find that when the environment of a two-level system has an energy spectrum with a lower bound but without an upper one, the survival probability of the spontaneous emission of the two-level system scales with the spatial dimension $D$ and the exponent $n$ of the energy dispersion $|\vec{k}|^n$ of the environment in the form $1-\alpha t^{2-D/n}$ in the short-time and in the form $\alpha t^{D/n-2}$ in the long-time regime. The former fractional scaling of the survival probability leads to a quantum Zeno effect with a different scaling of the Zeno time.