# Quantum Zeno effect in the multimode quantum Rabi model

## TL;DR

This paper investigates the quantum Zeno and anti-Zeno effects in the multimode quantum Rabi model, deriving analytical decay rates and exploring how cavity mode squeezing influences these quantum phenomena.

## Contribution

It provides an analytical expression for decay rates in the MQRM and explores the effects of squeezing, temperature, and high-frequency modes on the QZE and QAZE.

## Key findings

- Crossover from QZE to QAZE due to energy backflow.
- Decay rate depends on squeezing angle, strength, and temperature.
- Numerically exact methods confirm the analytical results.

## Abstract

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of the multimode quantum Rabi model(MQRM). We derive an analytic expression for the decay rate of the survival probability where cavity modes are initially prepared as thermal equilibrium states. A crossover from QZE to QAZE is observed due to the energy backflow induced by high frequency cavity modes. In addition, we apply a numerically exact method based on the thermofield dynamics(TFD) theory and the matrix product states(MPS) to study the effect of squeezing of the cavity modes on the QZE of the MQRM. The influence of the squeezing angle, squeezing strength and temperature on the decay rate of the survival probability are discussed.