# Dispersive Regimes of the Dicke Model

## TL;DR

This paper investigates two dispersive regimes of the Dicke model involving multiple atoms and a bosonic mode, revealing unexpected resonances and photon-number-dependent atomic dynamics through analytical and numerical methods.

## Contribution

It introduces analytical frameworks for understanding dispersive regimes in the Dicke model, including deep strong coupling and photon-number-dependent interactions, with new insights into resonance structures and atomic dynamics.

## Key findings

- Discovery of unexpected resonances for N≥2 in the deep strong coupling regime
- Demonstration that nontrivial dynamics occur in atomic degrees of freedom for specific Fock states
- Numerical verification of analytical predictions on qubit populations and photon statistics

## Abstract

We study two dispersive regimes in the dynamics of $N$ two-level atoms interacting with a bosonic mode for long interaction times. Firstly, we analyze the dispersive multiqubit quantum Rabi model for the regime in which the qubit frequencies are equal and smaller than the mode frequency, and for values of the coupling strength similar or larger than the mode frequency, namely, the deep strong coupling regime. Secondly, we address an interaction that is dependent on the photon number, where the coupling strength is comparable to the geometric mean of the qubit and mode frequencies. We show that the associated dynamics is analytically tractable and provide useful frameworks with which to analyze the system behavior. In the deep strong coupling regime, we unveil the structure of unexpected resonances for specific values of the coupling, present for $N\ge2$, and in the photon-number-dependent regime we demonstrate that all the nontrivial dynamical behavior occurs in the atomic degrees of freedom for a given Fock state. We verify these assertions with numerical simulations of the qubit population and photon-statistic dynamics.