A progressive diagonalization scheme for the Rabi Hamiltonian

TL;DR

This paper introduces a progressive diagonalization scheme for the Rabi Hamiltonian, enabling near-exact solutions for low-energy states with improved efficiency over traditional methods.

Contribution

A novel progressive diagonalization approach for the Rabi Hamiltonian that simplifies solving the model, especially for low-lying energy levels.

Findings

Efficient near-exact solutions for low-energy spectrum.

Comparison shows improved accuracy over generalized rotating-wave approximation.

Method reduces computational complexity for specific parameter sets.

Abstract

A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and full matrix diagonalization.