Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model

Cid Reyes-Bustos

doi:10.1007/978-981-15-5191-8_13

Abstract

AbstractThe quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter $$\varepsilon \in \mathbb {R}$$ ε ∈ R to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values $$\epsilon \in 1/2\mathbb {Z}$$ ϵ ∈ 1 / 2 Z via the study of the divisibility of the so-called constraint polynomials. In this article, we aim to provide further insight into the structure of Juddian solutions of the AQRM by extending the divisibility properties and the relations between the constraint polynomials with the solution of the AQRM in the Bargmann space. In particular we discuss a conjecture proposed by Masato Wakayama.

Highlights

The quantum Rabi model (QRM) is one of the basic models in quantum optics, describing the interaction between a two-level atom and a light field
In order to describe how the degeneracies in the spectrum of the asymmetric quantum Rabi model (AQRM) appear, we introduce the constraint polynomials
We expect that the results given here for constraint polynomials may provide some further insight for the studies in this direction

Summary

Introduction

The quantum Rabi model (QRM) is one of the basic models in quantum optics, describing the interaction between a two-level atom and a light field. HRabi is given by HRabi = ωa†a + g(a + a†)σx + σz, where a† and a are the creation and annihilation operators of the quantum harmonic oscillator, σx , σz are the Pauli matrices

Reyes-Bustos (B)

The Confluent Picture of the Asymmetric Quantum Rabi Model

Extended Divisibility Properties for Constraint and Related Polynomials

Number of Exceptional Solutions of the AQRM

Classification of Parameter Regimes