# The quantum Zeno and anti-Zeno effects with strong system-environment coupling

## TL;DR

This paper explores the quantum Zeno and anti-Zeno effects in strongly coupled systems, revealing that strong interactions lead to non-linear decay rates and indirect atom interactions, contrasting with weak coupling behaviors.

## Contribution

It introduces a polaron transformation approach to analyze the Zeno effects under strong system-environment coupling, highlighting qualitative and quantitative differences from weak coupling scenarios.

## Key findings

- Strong coupling alters the decay rate dependence on spectral density.
- Increasing coupling strength can decrease the effective decay rate.
- Collective interactions emerge among atoms via the common environment.

## Abstract

The fact that repeated projective measurements can slow down (the Zeno effect) or speed up (the anti-Zeno effect) quantum evolution is well-known. However, to date, studies of these effects focus on quantum systems that are weakly interacting with their environment. In this paper, we investigate what happens to a quantum system under the action of repeated measurements if the quantum system is strongly interacting with its environment. We consider as the quantum system a single two-level system coupled strongly to a collection of harmonic oscillators. A so-called polaron transformation is then used to make the problem in the strong system-environment coupling regime tractable. We find that the strong coupling case exhibits quantitative and qualitative differences as compared with the weak coupling case. In particular, the effective decay rate does not depend linearly on the spectral density of the environment. This then means that, in the strong coupling regime that we investigate, increasing the system-environment coupling strength can actually decrease the effective decay rate. We also consider a collection of two-level atoms coupled strongly with a common environment. In this case, we find that there are further differences between the weak and strong coupling cases since the two-level atoms can now indirectly interact with one another due to the common environment.