Criterion for quantum Zeno and anti-Zeno effects

TL;DR

This paper establishes a criterion based on the environmental spectral density's second derivative to predict quantum Zeno and anti-Zeno effects in a two-level system under measurement and environmental influence.

Contribution

It introduces a practical criterion for distinguishing Zeno effects based on spectral density curvature, applicable to various spectral environments.

Findings

Quantum Zeno effect occurs near resonance in Lorentzian spectra.

Anti-Zeno effect emerges off-resonance in Lorentzian spectra.

Sub-Ohmic environments favor Zeno effects; super-Ohmic favor anti-Zeno.

Abstract

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 function with respect to the system transition frequency is found to be a sufficient condition to distinguish between the quantum Zeno (negative) and the anti-Zeno (positive) effects raised by the measurements. We check our criterion for practical measurement intervals, which are larger than the conceptual Zeno time, in various environments. In particular, with the Lorentzian spectrum, the quantum Zeno and anti-Zeno phenomena are found to emerge respectively in the near-resonant and off-resonant cases. For the interacting spectra of hydrogenlike atoms, the quantum Zeno effect usually occurs and the anti-Zeno effect can rarely occur unless the transition frequency is close to the cut-off frequency. With a power-law spectrum, we find that sub-Ohmic and super-Ohmic environments lead to the quantum Zeno and anti-Zeno effects, respectively.