An exactly solvable system from quantum optics

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.

9 pages, 5 figures

References in corpus (1)

• Analytical method of spectra calculations in the Bargmann representation

Cited by in corpus (13)

• The quantum Rabi model: solution and dynamics
• Analytical method of spectra calculations in the Bargmann representation
• Entanglement resonance in the asymmetric quantum Rabi model
• Spectral determinant of the two-photon quantum Rabi model
• A novel approach to the spectral problem in the two photon Rabi model
• Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• Spectral continuum in the Rabi-Stark model
• Quantum Fisher information and polaron picture for identification of transition coupling in quantum Rabi model
• Dicke States Generation via Selective Interactions in Dicke-Stark Model
• Phase Transitions in the Anisotropic Dicke-Stark Model with $A$-square terms
• Solving and Completing the Rabi-Stark Model in the Ultrastrong Coupling Regime