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 $\left(\mathrm{\Lambda }\right)$, and find a perfect “scaling” property with the measurement frequency $\left({\tau }^{-1}\right)$ in terms of the scaling variable $x=\mathrm{\Lambda }\tau$. Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to $x\to \infty$ and $x\to 0$, respectively. This $x$-dependent criterion improves the idea of using $\tau$ alone and quantitatively identifies the validity condition of the conventional QT theory.

• Received 17 August 2015

DOI:https://doi.org/10.1103/PhysRevA.94.032130