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arXiv:1707.02578 · Science China Physics Mechanics and Astronomy

Theory for frequent measurements of spontaneous emissions in a non-Markovian environment: Beyond the Lorentzian spectrum

Luting Xu, Xin-Qi Li

Published Mar 27, 2019• 3 citations
arXivHTMLPDF
DOI
10.1007/s11433-019-9367-5

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In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth $(\mathrm{\ensuremath{\Lambda}})$, and find a perfect ``scaling'' property with the measurement frequency $({\ensuremath{\tau}}^{\ensuremath{-}1})$ in terms of the scaling variable $x=\mathrm{\ensuremath{\Lambda}}\ensuremath{\tau}$. Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to $x\ensuremath{\rightarrow}\ensuremath{\infty}$ and $x\ensuremath{\rightarrow}0$, respectively. This xxx-dependent criterion improves the idea of using $\ensuremath{\tau}$ alone and quantitatively identifies the validity condition of the conventional QT theory.