A hidden analytic structure of the Rabi model
Alexander Moroz

TL;DR
This paper reveals a hidden analytic structure of the Rabi model using orthogonal polynomials, enabling highly accurate energy level calculations and offering a new method for solving this quantum system.
Contribution
It introduces a novel analytic approach based on orthogonal polynomials to solve the Rabi model, surpassing previous methods in accuracy and computational efficiency.
Findings
Spectrum coincides with support of a discrete measure in orthogonality relations.
Allows calculation of up to 1350 energy levels with high precision.
Provides a new method for solving the Rabi model analytically.
Abstract
The Rabi model describes the simplest interaction between a cavity mode with a frequency and a two-level system with a resonance frequency . It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to , which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy , which are orthogonal on an equidistant lattice. A non-zero value of leads to non-classical discrete orthogonal polynomials and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model.…
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