Quantum trajectories under frequent measurements in a non-Markovian environment
Luting Xu, Xin-Qi Li · Physical Review A · 2016
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 $x$-dependent criterion improves the idea of using $\ensuremath{\tau}$ alone and quantitatively identifies the validity condition of the conventional QT theory.