Eigenvalues and Eigenstates of Quantum Rabi Model

TL;DR

This paper introduces an exact diagonalization method for the quantum Rabi model, enabling precise calculation of eigenvalues and eigenstates beyond the rotating wave approximation, with applications in quantum optics and related fields.

Contribution

The paper presents a novel approach based on Pauli operators for the exact diagonalization of the quantum Rabi Hamiltonian, extending solutions to regimes where the rotating wave approximation fails.

Findings

Eigenvalues and eigenstates of the quantum Rabi Hamiltonian are obtained.

The approach reproduces the Jaynes-Cummings solution as a special case.

Eigenstates can be expressed in the basis of Jaynes-Cummings eigenstates.

Abstract

The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to the need for the theoretical description of the interaction of a two-level system with a quantum oscillator in the case when the rotating wave approximation fails. In this Letter, we present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. This approach is based on the properties of the Pauli operators and allows us to readily solve the stationary Schrodinger equation for a two-level system. First, we demonstrate the applicability of the approach to the Jaynes-Cummings Hamiltonian to get the well-known solution. Then, we obtain the eigenvalues and eigenstates for the quantum Rabi Hamiltonian using the proposed approach. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.