# Monodromy in Dicke superradiance

## TL;DR

This paper investigates the monodromy phenomenon in an integrable Dicke model, revealing quantum signatures linked to superradiance and phase transitions, and examines how these structures break down under non-integrable perturbations.

## Contribution

It introduces the study of focus-focus monodromy in the Dicke model and connects classical and quantum signatures to superradiance and phase transitions.

## Key findings

- Quantum signatures of monodromy appear in eigenstate expectation values.
- Monodromy-related structures break down with increasing non-integrable perturbation.
- Connections between classical orbits and quantum phase transitions are established.

## Abstract

We study the focus-focus type of monodromy in an integrable version of the Dicke model. Classical orbits forming a pinched torus represent analogues of the dynamic superradiance under conditions of a closed system. Quantum signatures of monodromy appear in lattices of expectation values of various quantities in the Hamiltonian eigenstates and are related to an excited-state quantum phase transition. We demonstrate the breakdown of these structures with an increasing strength of non-integrable perturbation.