An exactly solvable system from quantum optics

TL;DR

This paper analyzes a generalized quantum optics model using differential equations, providing explicit formulas for its spectrum and eigenfunctions, and exploring its mathematical structure through the Stokes phenomenon and Galois theory.

Contribution

It introduces an exactly solvable quantum model in the Bargmann-Fock representation and derives explicit spectral formulas using asymptotic analysis.

Findings

Explicit spectrum and eigenfunctions derived

Connection between quantization and asymptotic behaviour established

Analysis of the differential Galois group provides mathematical insight

Abstract

We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given.