Analytical method of spectra calculations in the Bargmann representation

Understand

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.