Memory Effects in Spontaneous Emission Processes

Abstract

We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective two-level system with a vacuum decay rate ${\Gamma }_0$ and transition angular frequency ${\omega }_A$. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the {\it dimensionless} lifetime $\tau =t{\Gamma }_0$ of spontaneous emission, we obtain deviations from exponential decay of the form $\mathcal{O}(1/\tau )$ for the decay amplitude as well as the previously obtained asymptotic behaviors of the form $\mathcal{O}(1/{\tau }^2)$ or $\mathcal{O}(1/\tau {\ln }^2\tau )$ for $\tau \gg 1$. The actual asymptotic behavior depends on the adopted regularization procedure as well as on the physical parameters at hand. We show that for any reasonable range of $\tau$ and for a sufficiently large value of the required angular frequency cut-off ${\omega }_c$ of the electro-magnetic fluctuations, i.e. ${\omega }_c\gg {\omega }_A$, one obtains either a $\mathcal{O}(1/\tau )$ or a $\mathcal{O}(1/{\tau }^2)$ dependence. In the presence of physical boundaries, which can change the decay rate with many orders of magnitude, the conclusions remains the same after a suitable rescaling of parameters.

13 pages, 5 figures and 46 references

References in corpus (7)

• Bose-Einstein condensation on a superconducting atom chip
• Spin flip lifetimes in superconducting atom chips: BCS versus Eliashberg theory
• Measurement of the trapping lifetime close to a cold metallic surface on a cryogenic atom-chip
• Van der Waals interaction and spontaneous decay of an excited atom in a superlens-type geometry
• Microtraps for neutral atoms using superconducting structures in the critical state
• Is Radioactive Decay Really Exponential?
• Spontaneous Emission Near Superconducting Bodies

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