Quantum trajectories under frequent measurements in a non-Markovian environment

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