Quantum Zeno and anti-Zeno effects in open quantum systems

TL;DR

This paper investigates how memory effects in the environment influence quantum Zeno and anti-Zeno effects, revealing that traditional assumptions overlook time-dependent decay rates and measurement sensitivity, especially in systems with strong bath correlations.

Contribution

It demonstrates that environmental memory effects cause oscillatory and time-dependent decay rates, challenging traditional models and showing measurement number influences the quantum Zeno and anti-Zeno transition.

Findings

Decay rate is generally time-dependent or oscillatory.

Transition between QZE and QAZE depends on measurement count.

Results are applicable to realistic circuit QED systems.

Abstract

Traditional approach on quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in open quantum systems (implicitly) assumes the bath (environment) state returning to its original state after each instantaneous projective measurement on the system and thus ignores the cross-correlations of the bath operators between different Zeno intervals. However, this assumption is not generally true, especially for a bath with a considerably non-negligible memory effect and for a system repeatedly projected into an initial general superposition state. We find that in stark contrast to the result of a constant value found in the traditional approach, the scaled average decay rate in unit Zeno interval of the survival probability is generally time-dependent or has an oscillatory behavior. In the case of strong bath correlation, the transition between the QZE and QAZE depends sensitively on the number of measurements $N$. For a fixed $N$, a QZE region predicted by the tradition approach may be in fact already in the QAZE region. We illustrate our findings using an exactly solvable open qubit system model with a Lorentzian bath spectral density, which is directly related to realistic circuit cavity quantum electrodynamics systems. Thus the results and dynamics presented here can be verified by current superconducting circuit technology.