Criterion of quantum Zeno and anti-Zeno effects

Jia-Ming Zhang, Jun Jing, Li-Gang Wang, Shi-Yao Zhu

Published 2018-05-07Version 1

In this work, we study the decay behavior of a two-level system under the competing influence of a dissipative environment and repetitive measurements. The sign of the second derivative of the environmental spectral density with respect to the system transition frequency is found to be a sufficient condition to probe the quantum Zeno (negative) or the anti-Zeno (positive) effect raised by the measurements. We check our criterion for practical measurement intervals, which are much larger than the conceptual Zeno time, in various environments. In particular, with Lorentzian spectral density, the quantum Zeno and anti-Zeno phenomena are found to emerge respectively in the near-resonant and off-resonant cases. For interacting spectra of hydrogen-like atoms, the quantum anti-Zeno effect can occur when the transition frequency is near the cutoff frequency. With power-law spectrum, we find that sub-Ohmic and super-Ohmic environments lead to the quantum Zeno and anti-Zeno effects, respectively.