An exactly solvable system from quantum optics

•New exactly solvable system from quantum optics is found.•Normalisation condition for system in Bargmann representation is used.•Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.

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.