# Squeezed displaced entangled states in the quantum Rabi model

## TL;DR

This paper explores analytical solutions of the quantum Rabi model, revealing superpositions of displaced and squeezed states, and introduces a model interpolating between different spectral regimes to analyze spectral statistics.

## Contribution

It presents a novel single parameter model for the quantum Rabi model that bridges discrete and continuous spectra, analyzing spectral statistics near spectral collapse.

## Key findings

- Solutions are superpositions of displaced number and squeezed coherent states.
- Spectral statistics show interweaving fluctuations in first neighbor differences.
- Second neighbor separation remains constant near spectral collapse.

## Abstract

The quantum Rabi model accepts analytical solutions in the so-called degenerate qubit and relativistic regimes with discrete and continuous spectrum, in that order.We show that solutions in the laboratory frame are the superposition of even and odd displaced number states, in the former, and infinitely squeezed coherent states, in the latter, of the boson field correlated to the internal states of the qubit. We propose a single parameter model that interpolates between these discrete and continuous spectrum regimes to study the spectral statistics for first and second neighbor differences before the so-called spectral collapse. We find two central first neighbor differences that interweave and fluctuate keeping a constant second neighbor separation.