Analytical method of spectra calculations in the Bargmann representation

TL;DR

The paper introduces a universal analytical method for calculating spectra of quantum systems in the Bargmann representation, applicable to models like the Rabi model and its variants, by expressing spectra as zeros of transcendental functions.

Contribution

It develops a general approach to solve quantum systems in the Bargmann representation, linking spectra to zeros of explicit transcendental functions, including cases involving confluent Heun functions.

Findings

Spectra are zeros of transcendental functions.

Explicit formulas involve confluent Heun functions.

Method applies to various quantum models like Rabi models.

Abstract

We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one- and multi-photon Rabi models, or $N$ level systems interacting with a single mode of the electromagnetic field and their various generalizations. We explain three types of conditions that determine the spectrum and show their usage for two deformations of the Rabi model. We prove that the spectra of both models are just zeros of transcendental functions, which in one case are given explicitly in terms of confluent Heun functions.