A continued fraction based approach for the Two-photon Quantum Rabi Model

TL;DR

This paper introduces a continued fraction method to analyze the spectral properties of the Two-Photon Quantum Rabi Model, enabling precise detection of spectral collapse and aiding quantum simulations.

Contribution

The paper presents a novel continued fraction approach for the Two-Photon Quantum Rabi Model, improving numerical accuracy and providing a new technique to detect spectral collapse.

Findings

Spectral collapse can be identified via the large time limit of survival probability.

The continued fraction method achieves high numerical precision with large truncations.

The approach is validated against an exactly solvable case.

Abstract

We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model.